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Journal articles on the topic 'Limit Function'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Pereira, Olavo de Carvalho. "Limit calculation of a function without the use of ε and δ". Núcleo do Conhecimento 04, № 08 (2021): 05–31. https://doi.org/10.32749/nucleodoconhecimento.com.br/mathematical-olympiads/limit-calculation.

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The consulted bibliography does not present, in any of the analyzed cases, a calculation of the limit of a function, but only "shows" that the values presented as the "limit" satisfy the definition of limit of a function expressed through inequalities involving and , there is, therefore, a gap in this theme, which the present article comes to fill by fundamentally using the concept of defined function, as well as by identifying the expression " tends to a certain number" with a corresponding equality.

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2

Alifuddin, Moch, Mahmud Yunus, Mohamad Ilham Dwi Firmansyah, and Indra Cahya Ramdani. "Stieltjes Limits in Continuous Function Spaces." European Journal of Pure and Applied Mathematics 18, no. 2 (2025): 5909. https://doi.org/10.29020/nybg.ejpam.v18i2.5909.

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The concept of limits in calculus was first discovered by Sir Isaac Newton and Gottfried Wilhelm Leibniz in the late 17th century. Both developed calculus with different but complementary approaches and notations. The Stieltjes limit is a generalization of the conventional limit, where the limiter is a function. This study defines the limit and Stieltjes limit on function-valued operators, which are bounded operators whose limiters are continuous functions. To support this definition, we first introduce the concepts of neighborhoods, continuous function operators, increasing operators, strictl

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3

Tonra, Wilda Syam, Didi Suryadi, Kusnandi Kusnandi, and Endang Cahya Mulyaning. A. "Limit of Function Understanding by Student of National Mathematics Olimpiad ON MIPA in University." Sainsmat : Jurnal Ilmiah Ilmu Pengetahuan Alam 13, no. 2 (2024): 178. https://doi.org/10.35580/sainsmat132654872024.

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Limits of function is one of sub-topic of Calculus that is complex and difficult to understand. Several studies, both examining misconception and understanding related to function limits, aim to improve teaching and learning. This research is single Subject Research with a single subject, namely by Student of National Mathematics Olimpiad ON MIPA in University. Data was collected through a test instrument consisting of 7 questions on understanding function limits and interviews were conducted to confirm the subject's answers. Data analysis is qualitative. The research results show that 1) Subj

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4

Daniswara, Krisna Adilia, Aris Alfan, and Ahmad Khairul Umam. "The Fifth Coefficient Approximation of The Inverse Strongly Convex Function." Jurnal Matematika Sains dan Teknologi 24, no. 2 (2023): 62–72. http://dx.doi.org/10.33830/jmst.v24i2.4977.2023.

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This paper discusses the fifth coefficient approximation of the inverse strongly convex function. Strongly convex function is a subclass of convex function. Those functions are included as univalent functions. Using corresponding lemmas, we give sharp limits for the fifth coefficient of the inverse strongly convex function. The limit is sharp if the value of the approximation has the same value as the limit. We verify that the limit of the fifth coefficient of the inverse strongly convex function differs from that of the strongly convex function in some interval but still have the same value i

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Hajerina, Hajerina, Sutji Rochaminah, and Indah Suciati. "Analyzing Mathematics Education Students' Misconceptions on Limit Functions : A Case Study at Alkhairaat University." Jurnal Pendidikan MIPA 26, no. 1 (2025): 51–61. https://doi.org/10.23960/jpmipa.v26i1.pp51-61.

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Abstract: The purpose of this study was to determine the misconceptions made by Unisa Mathematics Education students about the concept of limit. The research method used was a descriptive qualitative approach or survey design, where data were collected through comprehension tests, interviews, and observations of 16 students. The results showed that students consider limit as something that is not reached, limit is an estimate, limit is a boundary, and a function will always have a limit at a certain point. Other misconceptions are that students consider limit as a substitution process, even th

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Sangwin, Christopher J. "Limit-free derivatives." Mathematical Gazette 95, no. 534 (2011): 469–82. http://dx.doi.org/10.1017/s0025557200003569.

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Algebraic double roots are used by [1] to motivate the following limit-free definition of derivative:‘A function f(x) has a derivative m at x = a iffor some value c.’As we shall see later, ‘function’ in this definition will actually be restricted to real polynomials and [1] concludes‘We have shown how an elementary algebraic principle — double roots — can lead to a complete calculus of polynomials and related functions, without the need for a limit concept.

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7

Sulastri, Rini. "Studi didactic transposition: Eksplorasi knowledge to be taught pada limit fungsi." Journal of Didactic Mathematics 4, no. 2 (2023): 106–17. http://dx.doi.org/10.34007/jdm.v4i2.1903.

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The purpose of this research is to describe the analysis of knowledge to be taught on limit of function. This research is part of the didactic transposition research on the concept of limit of function which consists of four stages. Qualitative research with descriptive method is used in this study. The target is a differential calculus course taught in the first semester at a university in Aceh. Data collection techniques consist of documentation studies and unstructured interviews. Analysis of calculus text book documents, especially on limit functions, was carried out using a praxeology app

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8

Xu, Xinyao. "Evaluation of limits including integrals by L Hpitals rule." Theoretical and Natural Science 10, no. 1 (2023): 96–100. http://dx.doi.org/10.54254/2753-8818/10/20230323.

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Limit is significant concept in mathematic analysis. Technically, limits definition in mathematics is that a variable in a function gradually approximates to a certain value in the changing process which cannot be ended. L Hpitals rule and Taylor expansion, together with other methods such as Stolz theorem, are usually used in measuring a limits value. In this paper, it will focus on some representative limits that are related to definite integrals. L Hpitals rule and Taylor's expansion are also jointed used so as to solve the problems. The main part of this work talks about the limit of the i

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9

Agustin Dewanti Putri, Walter Punding, and M. Hamdani. "Identification of Students' Mistakes in Solving the Limit Function Problems for Class XI SMA Negeri 1 Palangka Raya." GAMAPROIONUKLEUS 2, no. 2 (2021): 78–84. http://dx.doi.org/10.37304/jpmipa.v2i2.5043.

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This research is motivated by the fact that many students of class XI make mistakes in solving the Limit Function problem. The aims of this research are 1) to describe the mistakes made by the students of class XI MIPA 2 SMA Negeri 1 Palangka Raya in solving Function Limit questions; 2) describe the cause of students in class XI MIPA 2 SMA Negeri 1 Palangka Raya making mistakes in solving Function Limit questions. The type of research used in this research is descriptive with a qualitative approach. This research was conducted in the even semester of the 2020/2021 academic year. The subj

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10

Rogeon, Philippe, and Hassan Emamirad. "Semiclassical limit of Husimi function." Discrete and Continuous Dynamical Systems - Series S 6, no. 3 (2012): 669–76. http://dx.doi.org/10.3934/dcdss.2013.6.669.

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11

Borsík. "Limit of Simply Continuous Function." Real Analysis Exchange 18, no. 1 (1992): 270. http://dx.doi.org/10.2307/44133069.

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12

Zhang, C. "New Limit Power Function Spaces." IEEE Transactions on Automatic Control 49, no. 5 (2004): 763–66. http://dx.doi.org/10.1109/tac.2004.825970.

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13

Chen, Chung-Ho. "SPECIFICATION LIMIT UNDER MEMBERSHIP FUNCTION." Quality Engineering 12, no. 4 (2000): 519–21. http://dx.doi.org/10.1080/08982110008962617.

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14

Kim, Honggie, Yun Hee Lee, Hee Sung Shin, and Sounki Lee. "Influence Function on Tolerance Limit." Communications for Statistical Applications and Methods 10, no. 2 (2003): 497–505. http://dx.doi.org/10.5351/ckss.2003.10.2.497.

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15

Pan, Xuezai, and Xudong Shang. "The Uniform Convergence Property of Sequence of Fractal Interpolation Functions in Complicated Networks." Mathematics 10, no. 20 (2022): 3834. http://dx.doi.org/10.3390/math10203834.

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In order to further research the relationship between fractals and complicated networks in terms of self-similarity, the uniform convergence property of the sequence of fractal interpolation functions which can generate self-similar graphics through iterated function system defined by affine transformation is studied in this paper. The result illustrates that it is can be proved that the sequence of fractal interpolation functions uniformly converges to its limit function and its limit function is continuous and integrable over a closed interval under the uniformly convergent condition of the

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16

LIVCHAK, J. "A NOTE ON ALGEBRAIC LIMIT OF A REAL FUNCTION." International Journal of Algebra and Computation 17, no. 05n06 (2007): 1067–71. http://dx.doi.org/10.1142/s0218196707004062.

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A new viewpoint on the notion of the limit of a function is proposed. We define a series of algebraic limit transitions of a function and prove that every real function has a number of non-trivial algebraic limits.

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17

Amen, Azad Ibrahim. "On Limit Cycles of Planar Dynamical System Via Dulac- Cherkas Function." Journal of Zankoy Sulaimani - Part A 17, no. 2 (2015): 45–50. http://dx.doi.org/10.17656/jzs.10379.

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18

widodo, winarso, and Toheri Toheri. "A case study of misconceptions students in the learning of mathematics; The concept limit function in high school." Jurnal Riset Pendidikan Matematika 4, no. 1 (2017): 120–27. https://doi.org/10.5281/zenodo.802250.

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This study aims to find out how high the level and trends of student misconceptions experienced by high school students in Indonesia. The subject of research that is a class XI student of Natural Science (IPA) SMA Negeri 1 Anjatan with the subject matter limit function. Forms of research used in this study is a qualitative research, with a strategy that is descriptive qualitative research. The data analysis focused on the results of the students' answers on the test essay subject matter limit function with the number of students by 16 (sixteen). Data collection techniques used are shaped test

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19

Zhang, Chuanyi, and Weiguo Liu. "Uniform limit power-type function spaces." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–14. http://dx.doi.org/10.1155/ijmms/2006/17042.

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To answer a question proposed by Mari in 1996, we propose&#x1D4B0;ℒ&#x1D4AB;α(ℝ+), the space of uniform limit power functions. We show that&#x1D4B0;ℒ&#x1D4AB;α(ℝ+)has properties similar to that of&#x1D49C;&#x1D4AB;(ℝ+). We also proposed three other limit power function spaces.

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20

Diah, Mohamad Nur, Magdalena Dhema, and Agustinus Angelaus Ete. "Analysis of Student Errors in Solving Math Problems for Class XII of Nursing Assistant at St. Thomas Maumere Vocational High School." EduMatika: Jurnal MIPA 3, no. 1 (2023): 20–27. http://dx.doi.org/10.56495/emju.v3i1.342.

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This study analyzes students' mistakes in doing math problems on function limit material. This research was conducted at SMK Santo Thomas Maumere in semester 2 of the 2021/2022 academic year. This type of research is qualitative research. The subjects of the study were 3 students drawn from 26 students of class XII Nursing Assistants. The results of this study show that the types of mistakes made by students are fact, conceptual, principle, and procedural errors based on the classification of fundamental errors of mathematical objects. The factual error made by students is that students are mi

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21

Tavakoli, Kourosh. "Boundary points as limit functions of iterated holomorphic function systems." Proceedings of the American Mathematical Society 137, no. 06 (2009): 1971–76. http://dx.doi.org/10.1090/s0002-9939-09-09683-x.

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22

Riesa Riskania Yuniman, Fikri Bakti Ridayana, Kristina Siagian, Dinda Nurfadilah, and Ahmad Fu’adin. "Penerapan Konsep Limit Fungsi dalam Kehidupan." JURNAL RISET RUMPUN MATEMATIKA DAN ILMU PENGETAHUAN ALAM 1, no. 2 (2022): 187–94. http://dx.doi.org/10.55606/jurrimipa.v1i2.616.

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Limit of a function is the main of calculus that teached in high school. The concept is the value of a function gets closer or approaches some number. This research focuses on finding the use of the limit function concept in every sectors in our daily, inside and outside the mathematic. This research was conducted to increase motivation to students in studying limit of functions in school and to become a source of knowledge for others. The research method used is study literature. The result of this reseach is the concept of limit function widely used in various sectors of life. In engineering

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23

Rösler, Margit, Tom Koornwinder, and Michael Voit. "Limit transition between hypergeometric functions of type BC and type A." Compositio Mathematica 149, no. 8 (2013): 1381–400. http://dx.doi.org/10.1112/s0010437x13007045.

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AbstractLet ${F}_{BC} (\lambda , k; t)$ be the Heckman–Opdam hypergeometric function of type BC with multiplicities $k= ({k}_{1} , {k}_{2} , {k}_{3} )$ and weighted half-sum $\rho (k)$ of positive roots. We prove that ${F}_{BC} (\lambda + \rho (k), k; t)$ converges as ${k}_{1} + {k}_{2} \rightarrow \infty $ and ${k}_{1} / {k}_{2} \rightarrow \infty $ to a function of type A for $t\in { \mathbb{R} }^{n} $ and $\lambda \in { \mathbb{C} }^{n} $. This limit is obtained from a corresponding result for Jacobi polynomials of type BC, which is proven for a slightly more general limit behavior of the m

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24

Gordon, Russell A. "When Is a Limit Function Continuous?" Mathematics Magazine 71, no. 4 (1998): 306. http://dx.doi.org/10.2307/2690707.

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25

Gordon, Russell A. "When is a Limit Function Continuous?" Mathematics Magazine 71, no. 4 (1998): 306–8. http://dx.doi.org/10.1080/0025570x.1998.11996660.

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26

Hwang, J. H., B. U. Park, and W. Ryu. "Limit theorems for boundary function estimators." Statistics & Probability Letters 59, no. 4 (2002): 353–60. http://dx.doi.org/10.1016/s0167-7152(02)00211-0.

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27

Camargo, Javier, та Johan Cancino. "The ω-limit function on dendrites". Topology and its Applications 282 (серпень 2020): 107320. http://dx.doi.org/10.1016/j.topol.2020.107320.

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28

Djurdje Cvijović and Hari M. Srivastava. "Limit Representations of Riemann’s Zeta Function." American Mathematical Monthly 119, no. 4 (2012): 324. http://dx.doi.org/10.4169/amer.math.monthly.119.04.324.

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29

Durot, Cécile, and Hendrik P. Lopuhaä. "Limit Theory in Monotone Function Estimation." Statistical Science 33, no. 4 (2018): 547–67. http://dx.doi.org/10.1214/18-sts664.

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30

Cu, Thi Kim Dung, Thi Thu Hien Nguyen, and Thi Thu Thuy Nguyen. "Topological Essence of the Concept "Limit of a Function" in the General Mathematics." RA JOURNAL OF APPLIED RESEARCH 07, no. 12 (2021): 2741–44. https://doi.org/10.5281/zenodo.5773722.

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ABSTRACT: The limit of a function is one of the most important concepts in high school mathematics. But unfortunately, not many students understand the essence of this concept. They had to accept it. This paper presents the topological essence of a limit of a function and discusses methods for teaching this concept in general education in Viet Nam. It consists of four parts. Part 1 talks about the definition of “Limit of a function”, part 2 covers the Mathematical essence of the concept limit of a function, part 3 deals with Defining the limit of a function in a topological space o

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31

Wu, Wei Biao, and Michael Woodroofe. "A central limit theorem for iterated random functions." Journal of Applied Probability 37, no. 3 (2000): 748–55. http://dx.doi.org/10.1239/jap/1014842833.

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A central limit theorem is established for additive functions of a Markov chain that can be constructed as an iterated random function. The result goes beyond earlier work by relaxing the continuity conditions imposed on the additive function, and by relaxing moment conditions related to the random function. It is illustrated by an application to a Markov chain related to fractals.

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Wu, Wei Biao, and Michael Woodroofe. "A central limit theorem for iterated random functions." Journal of Applied Probability 37, no. 03 (2000): 748–55. http://dx.doi.org/10.1017/s0021900200015965.

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A central limit theorem is established for additive functions of a Markov chain that can be constructed as an iterated random function. The result goes beyond earlier work by relaxing the continuity conditions imposed on the additive function, and by relaxing moment conditions related to the random function. It is illustrated by an application to a Markov chain related to fractals.

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33

Arnal-Palacián, Mónica. "Infinite limit of a function at infinity and its phenomenology." Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia 14 (December 31, 2022): 25–41. http://dx.doi.org/10.24917/20809751.14.3.

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In this paper we aim to characterise and define the phenomena of the infinite limit of a function at infinity. Based on the intuitive and formal approaches, we obtain as results five phenomena organised by a definition of this limit: intuitive unlimited growth of a function, for plus and minus infinity, and intuitive unlimited decrease of a function, for plus and minus infinity (intuitive approach), and the round-trip phenomenon of infinite limit functions (formal approach). All this is intended to help overcome the difficulties that pre-university students have with the concept of limit, cont

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Daujanov, Ainazar Shinnazarovich, Aysanem Kuanishbaevna Turganbaeva, Muxtorbek Raximboyev, and Aynura Xiyasova. "LINEAR CHANGE OF VARIABLES AND ON SIMPLIFICATION OF EXPRESSIONS IN THE SPACE OF GENERALIZED FUNCTIONS." EURASIAN JOURNAL OF ACADEMIC RESEARCH 1, no. 1 (2021): 971–76. https://doi.org/10.5281/zenodo.4742240.

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<em>The rigorous mathematical theory of generalized functions contains the definition of a set of basic functions, the definition of a continuous functional, rules for performing limit transitions, delta-like sequences, etc. Special literature is devoted to these questions, in which one can find formulations and proofs of the corresponding theorems (see, for example, the book by V.S. Vladimirov "Generalized functions in mathematical physics", I.M. Gelfand and G.E.Shilov "Generalized functions and actions on them ", MS Agranovich" Generalized functions and Sobolev space

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35

Kharazishvili, Alexander. "On finite sums of periodic functions." Georgian Mathematical Journal 27, no. 2 (2020): 265–69. http://dx.doi.org/10.1515/gmj-2019-2076.

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AbstractIt is shown that any function acting from the real line {\mathbb{R}} into itself can be expressed as a pointwise limit of finite sums of periodic functions. At the same time, the real analytic function {x\rightarrow\exp(x^{2})} cannot be represented as a uniform limit of finite sums of periodic functions and, simultaneously, this function is a locally uniform limit of finite sums of periodic functions. The latter fact needs the techniques of Hamel bases.

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36

Hubal, Halyna. "ANALYSIS OF APPROACHES TO THE STUDY OF LIMITS OF SEQUENCES AND FUNCTIONS AND THE USE OF INFORMATION TECHNOLOGIES." Grail of Science, no. 35 (January 25, 2024): 226–31. http://dx.doi.org/10.36074/grail-of-science.19.01.2024.040.

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Article analyzes approaches to the study of limits of sequences and functions and the use of information technologies. The theorem on the limit of an intermediate sequence is of great importance when investigating the convergence of sequences and when calculating the limits of sequences. It is developed an algorithm for applying this theorem that is illustrated with examples. An example of calculating the limit of a function with a geometric interpretation of the obtained result is considered. The possibility of completing the calculation of limits at infinity, using the program code written b

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Abbood Altai, Abdulhameed Qahtan. "FUZZY LIMITS OF FUZZY FUNCTIONS." Malaysian Journal of Science 40, no. 3 (2021): 76–106. http://dx.doi.org/10.22452/mjs.vol40no3.7.

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In this paper, we study the theory of fuzzy limit of fuzzy function depending on the Altai’s principle and using the representation theorem (resolution principle) to run the fuzzy arithmetic.The novelty underlying this theory is that we can provethe convergence of afuzzy function to its fuzzy limit through proving the convergence of its 𝛼-cuts’boundaries to their limits for the membership degree 0<𝛼𝑜<𝛼1≤𝛼≤1.

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38

Ouyang, Qi, Xiao Qian Chen, and Wen Yao. "Comparison of the Function Regression Method and Data Classification Method for Limit State Function Approximation." Advanced Materials Research 774-776 (September 2013): 1738–44. http://dx.doi.org/10.4028/www.scientific.net/amr.774-776.1738.

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To reduce the computational burden of the reliability analysis of complex engineering application, approximate method is always used to construct the surrogate model of the implicit limit state function. Since the limit state function is a classifier of the failure domain and safe domain, its approximation can be established by the function regression method and data classification method. In this paper, these two methods are tested to several limit state functions including linear function, highly nonlinear function, high dimensional function, series system and parallel system. Least squares

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39

Albayrak, Hüseyin, and Serpil Pehlivan. "The set of filter cluster functions." Filomat 32, no. 9 (2018): 3057–71. http://dx.doi.org/10.2298/fil1809057a.

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In this work, we are concerned with the concepts of F-?-convergence, F-pointwise convergence and F-uniform convergence for sequences of functions on metric spaces, where F is a filter on N. We define the concepts of F-limit function, F-cluster function and limit function respectively for each of these three types of convergence, and obtain some results about the sets of F-cluster and F-limit functions for sequences of functions on metric spaces. We use the concept of F-exhaustiveness to characterize the relations between these points.

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Mortenson, Eric. "Ramanujan's Radial Limits and Mixed Mock Modular Bilateralq-Hypergeometric Series." Proceedings of the Edinburgh Mathematical Society 59, no. 3 (2015): 787–99. http://dx.doi.org/10.1017/s0013091515000425.

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AbstractUsing results from Ramanujan's lost notebook, Zudilin recently gave an insightful proof of a radial limit result of Folsomet al.for mock theta functions. Here we see that Mortenson's previous work on the dual nature of Appell–Lerch sums and partial theta functions and on constructing bilateralq-series with mixed mock modular behaviour is well suited for such radial limits. We present five more radial limit results, which follow from mixed mock modular bilateralq-hypergeometric series. We also obtain the mixed mock modular bilateral series for a universal mock theta function of Gordon a

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41

Serfozo, Richard F. "Applications of the key renewal theorem: crudely regenerative processes." Journal of Applied Probability 29, no. 2 (1992): 384–95. http://dx.doi.org/10.2307/3214575.

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Limit Statements obtainable by the key renewal theorem are of the form EXt = v(t) + o(1), as t →∞. We show how to delineate the limit function v for processes X associated with crudely regenerative phenomena. Included are refinements of classical limit theorems for Markov and regenerative processes, limits of sums of stationary random variables, and limits for integrals and derivatives of EXt.

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Serfozo, Richard F. "Applications of the key renewal theorem: crudely regenerative processes." Journal of Applied Probability 29, no. 02 (1992): 384–95. http://dx.doi.org/10.1017/s0021900200043138.

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Limit Statements obtainable by the key renewal theorem are of the form EXt = v(t) + o(1), as t →∞. We show how to delineate the limit function v for processes X associated with crudely regenerative phenomena. Included are refinements of classical limit theorems for Markov and regenerative processes, limits of sums of stationary random variables, and limits for integrals and derivatives of EXt.

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43

Loocke, Philip Van. "Fields as Limit Functions of Stochastic Discrimination and Their Adaptability." Neural Computation 14, no. 5 (2002): 1059–70. http://dx.doi.org/10.1162/089976602753633385.

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For a particular type of elementary function, stochastic discrimination is shown to have an analytic limit function. Classifications can be performed directly by this limit function instead of by a sampling procedure. The limit function has an interpretation in terms of fields that originate from the training examples of a classification problem. Fields depend on the global configuration of the training points. The classification of a point in input space is known when the contributions of all fields are summed. Two modifications of the limit function are proposed. First, for nonlinear problem

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44

Andrews, Patricia L., Miguel G. Cruz, and Richard C. Rothermel. "Examination of the wind speed limit function in the Rothermel surface fire spread model." International Journal of Wildland Fire 22, no. 7 (2013): 959. http://dx.doi.org/10.1071/wf12122.

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The Rothermel surface fire spread model includes a wind speed limit, above which predicted rate of spread is constant. Complete derivation of the wind limit as a function of reaction intensity is given, along with an alternate result based on a changed assumption. Evidence indicates that both the original and the revised wind limits are too restrictive. Wind limit is based in part on data collected on the 7 February 1967 Tasmanian grassland fires. A reanalysis of the data indicates that these fires might not have been spreading in fully cured continuous grasslands, as assumed. In addition, mor

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45

Kalinkin, A. V., and A. V. Mastikhin. "A Limit Theorem for a Weiss Epidemic Process." Journal of Applied Probability 52, no. 1 (2015): 247–57. http://dx.doi.org/10.1239/jap/1429282619.

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For a Markov two-dimensional death-process of a special class we consider the use of Fourier methods to obtain an exact solution of the Kolmogorov equations for the exponential (double) generating function of the transition probabilities. Using special functions, we obtain an integral representation for the generating function of the transition probabilities. We state the expression of the expectation and variance of the stochastic process and establish a limit theorem.

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Kalinkin, A. V., and A. V. Mastikhin. "A Limit Theorem for a Weiss Epidemic Process." Journal of Applied Probability 52, no. 01 (2015): 247–57. http://dx.doi.org/10.1017/s0021900200012328.

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For a Markov two-dimensional death-process of a special class we consider the use of Fourier methods to obtain an exact solution of the Kolmogorov equations for the exponential (double) generating function of the transition probabilities. Using special functions, we obtain an integral representation for the generating function of the transition probabilities. We state the expression of the expectation and variance of the stochastic process and establish a limit theorem.

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47

Laurinčikas, Antanas. "Limit theorems for the Matsumoto zeta-function." Journal de Théorie des Nombres de Bordeaux 8, no. 1 (1996): 143–58. http://dx.doi.org/10.5802/jtnb.161.

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48

Wei, Fu-Tsun. "Kronecker limit formula over global function fields." American Journal of Mathematics 139, no. 4 (2017): 1047–84. http://dx.doi.org/10.1353/ajm.2017.0027.

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Seglar, Pere, and Enric Pérez. "Classical limit of the canonical partition function." European Journal of Physics 35, no. 1 (2013): 015004. http://dx.doi.org/10.1088/0143-0807/35/1/015004.

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McWhorter, Todd J., and Carlos Martínez del Rio. "Does Gut Function Limit Hummingbird Food Intake?" Physiological and Biochemical Zoology 73, no. 3 (2000): 313–24. http://dx.doi.org/10.1086/316753.

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