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Journal articles on the topic 'Umbral calculus'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 March 2023

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1

Kim, K. H. "The Umbral Calculus." Mathematical Social Sciences 11, no. 1 (1986): 94–95. http://dx.doi.org/10.1016/0165-4896(86)90009-0.

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2

Yun, Sang Jo, та Jin-Woo Park. "Identities of Degenerate Poly-Changhee Polynomials Arising from λ -Sheffer Sequences". Journal of Mathematics 2022 (14 липня 2022): 1–9. http://dx.doi.org/10.1155/2022/1482534.

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In the 1970s, Gian-Carlo Rota constructed the umbral calculus for investigating the properties of special functions, and by Kim-Kim, umbral calculus is generalized called λ -umbral calculus. In this paper, we find some important relationships between degenerate Changhee polynomials and some important special polynomials by expressing the Changhee polynomial as a linear combination of some special polynomials. In addition, we derive some interesting identities related to degenerate poly-Changhee polynomials and some important special functions by using λ -umbral calculus.

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3

Rota, G. C., and B. D. Taylor. "The Classical Umbral Calculus." SIAM Journal on Mathematical Analysis 25, no. 2 (1994): 694–711. http://dx.doi.org/10.1137/s0036141093245616.

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4

Verdoodt, Ann. "Non-Archimedean Umbral Calculus." Annales mathématiques Blaise Pascal 5, no. 1 (1998): 55–73. http://dx.doi.org/10.5802/ambp.105.

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5

Sun, Xie-Hua. "On Umbral Calculus I." Journal of Mathematical Analysis and Applications 244, no. 2 (2000): 279–90. http://dx.doi.org/10.1006/jmaa.1999.6686.

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6

Verdoodt, Ann. "p-adicq-umbral Calculus." Journal of Mathematical Analysis and Applications 198, no. 1 (1996): 166–77. http://dx.doi.org/10.1006/jmaa.1996.0074.

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7

Benyattou, Abdelkader. "Congruences via umbral calculus." Notes on Number Theory and Discrete Mathematics 28, no. 4 (2022): 719–29. http://dx.doi.org/10.7546/nntdm.2022.28.4.719-729.

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In this paper, we use the properties of the classical umbral calculus to give some congruences related to the Bell numbers and Bell polynomials. We also present a new congruence involving Appell polynomials with integer coefficients.

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8

Roman, Steven. "More on the umbral calculus, with emphasis on the q-umbral calculus." Journal of Mathematical Analysis and Applications 107, no. 1 (1985): 222–54. http://dx.doi.org/10.1016/0022-247x(85)90367-1.

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9

Zeilberger, Doron. "Book Review: The umbral calculus." Bulletin of the American Mathematical Society 13, no. 1 (1985): 73–77. http://dx.doi.org/10.1090/s0273-0979-1985-15374-1.

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10

López-Sendino, J. E., J. Negro, M. A. del Olmo, and E. Salgado. "Quantum mechanics and umbral calculus." Journal of Physics: Conference Series 128 (August 1, 2008): 012056. http://dx.doi.org/10.1088/1742-6596/128/1/012056.

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11

Benouaret, Chahrazed, and Alain Salinier. "Umbral calculus in Ore extensions." Journal of Pure and Applied Algebra 224, no. 3 (2020): 958–86. http://dx.doi.org/10.1016/j.jpaa.2019.06.017.

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12

Ueno, Kazuo. "Umbral calculus and special functions." Advances in Mathematics 67, no. 2 (1988): 174–229. http://dx.doi.org/10.1016/0001-8708(88)90040-0.

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13

Finkelshtein, Dmitri, Yuri Kondratiev, Eugene Lytvynov, and Maria João Oliveira. "An infinite dimensional umbral calculus." Journal of Functional Analysis 276, no. 12 (2019): 3714–66. http://dx.doi.org/10.1016/j.jfa.2019.03.006.

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14

Kochubei, Anatoly N. "Umbral calculus in positive characteristic." Advances in Applied Mathematics 34, no. 1 (2005): 175–91. http://dx.doi.org/10.1016/j.aam.2004.07.004.

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15

Bottreau, A., A. Di Bucchianico, and D. E. Loeb. "Computer algebra and Umbral Calculus." Discrete Mathematics 180, no. 1-3 (1998): 65–72. http://dx.doi.org/10.1016/s0012-365x(97)00108-8.

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16

Gzyl, Henryk. "Umbral calculus via integral transforms." Journal of Mathematical Analysis and Applications 129, no. 2 (1988): 315–25. http://dx.doi.org/10.1016/0022-247x(88)90252-1.

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17

Behr, Nicolas, Giuseppe Dattoli, Ambra Lattanzi, and Silvia Licciardi. "Dual Numbers and Operational Umbral Methods." Axioms 8, no. 3 (2019): 77. http://dx.doi.org/10.3390/axioms8030077.

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Dual numbers and their higher-order version are important tools for numerical computations, and in particular for finite difference calculus. Based on the relevant algebraic rules and matrix realizations of dual numbers, we present a novel point of view, embedding dual numbers within a formalism reminiscent of operational umbral calculus.

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18

Dere, Rahime. "Some Hermite base polynomials on q-umbral algebra." Filomat 30, no. 4 (2016): 961–67. http://dx.doi.org/10.2298/fil1604961d.

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The aim of this paper is to investigate the q-Hermite type polynomials by using umbral calculus methods. Using this method, we derive new type polynomials which are related to the q-Bernoulli polynomials and the q-Hermite type polynomials. Furthermore, we also derive some new identities of those polynomials which are derived from q-umbral calculus.

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19

Diarra, Bertin. "Ultrametric umbral calculus in characteristic $p$." Bulletin of the Belgian Mathematical Society - Simon Stevin 14, no. 5 (2007): 845–69. http://dx.doi.org/10.36045/bbms/1197908899.

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20

Kholodov, Alexander Nickolaevich. "The umbral calculus on logarithmic algebras." Acta Applicandae Mathematicae 19, no. 1 (1990): 55–76. http://dx.doi.org/10.1007/bf00047231.

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21

Kholodov, Alexander Nickolaevich. "The umbral calculus and orthogonal polynomials." Acta Applicandae Mathematicae 19, no. 1 (1990): 1–54. http://dx.doi.org/10.1007/bf00047230.

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22

Kim, Dae San, and Taekyun Kim. "Umbral calculus associated with Bernoulli polynomials." Journal of Number Theory 147 (February 2015): 871–82. http://dx.doi.org/10.1016/j.jnt.2013.09.013.

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23

Razpet, Marko. "An application of the umbral calculus." Journal of Mathematical Analysis and Applications 149, no. 1 (1990): 1–16. http://dx.doi.org/10.1016/0022-247x(90)90281-j.

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24

Kisil, V. V. "Umbral Calculus and Cancellative Semigroup Algebras." Zeitschrift für Analysis und ihre Anwendungen 19, no. 2 (2000): 315–38. http://dx.doi.org/10.4171/zaa/953.

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25

Hammouch, H. "Umbral Calculus, Martingales, and Associated Polynomials." Stochastic Analysis and Applications 22, no. 2 (2004): 443–47. http://dx.doi.org/10.1081/sap-120028600.

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26

Méndez, Miguel A. "The Umbral Calculus of Symmetric Functions." Advances in Mathematics 124, no. 2 (1996): 207–71. http://dx.doi.org/10.1006/aima.1996.0083.

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27

Gessel, Ira M. "Applications of the classical umbral calculus." Algebra Universalis 49, no. 4 (2003): 397–434. http://dx.doi.org/10.1007/s00012-003-1813-5.

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28

Niederhausen, Heinrich. "Rota?s umbral calculus and recursions." Algebra Universalis 49, no. 4 (2003): 435–57. http://dx.doi.org/10.1007/s00012-003-1820-6.

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29

Guo, Li. "Baxter Algebras and the Umbral Calculus." Advances in Applied Mathematics 27, no. 2-3 (2001): 405–26. http://dx.doi.org/10.1006/aama.2001.0742.

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30

Maheswaran, A., and C. Elango. "Effect of Delta Operator on Umbral Composition in Finite Operator calculus." JOURNAL OF ADVANCES IN MATHEMATICS 12, no. 7 (2016): 6392–97. http://dx.doi.org/10.24297/jam.v12i7.5482.

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The main objective of this paper is to propose the matrix representation of umbral composition and investigate the effect of delta operator on umbral composition by using the sequential representation of delta operator in finite operator calculus.

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31

Kim, Dae San, and Taekyun Kim. "Applications of Umbral Calculus Associated withp-Adic Invariant Integrals onZp." Abstract and Applied Analysis 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/865721.

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Recently, Dere and Simsek (2012) have studied the applications of umbral algebra to some special functions. In this paper, we investigate some properties of umbral calculus associated withp-adic invariant integrals onZp. From our properties, we can also derive some interesting identities of Bernoulli polynomials.

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32

Kim, Taekyun, Dae San Kim, Toufik Mansour, Seog-Hoon Rim, and Matthias Schork. "Umbral calculus and Sheffer sequences of polynomials." Journal of Mathematical Physics 54, no. 8 (2013): 083504. http://dx.doi.org/10.1063/1.4817853.

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33

Dattoli, G., D. Levi, and P. Winternitz. "Heisenberg algebra, umbral calculus and orthogonal polynomials." Journal of Mathematical Physics 49, no. 5 (2008): 053509. http://dx.doi.org/10.1063/1.2909731.

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34

Ray, Nigel. "Umbral calculus, binomial enumeration and chromatic polynomials." Transactions of the American Mathematical Society 309, no. 1 (1988): 191. http://dx.doi.org/10.1090/s0002-9947-1988-0957067-0.

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35

Chen, William Y. C., H. W. Galbraith, and J. D. Louck. "Angular momentum theory, umbral calculus, and combinatorics." Computers & Mathematics with Applications 41, no. 9 (2001): 1199–214. http://dx.doi.org/10.1016/s0898-1221(01)00091-8.

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36

Kim, Dae San, and Tae Kyun Kim. "q-Bernoulli polynomials and q-umbral calculus." Science China Mathematics 57, no. 9 (2014): 1867–74. http://dx.doi.org/10.1007/s11425-014-4821-3.

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37

Kim, Dae San, Taekyun Kim, and Sang-Hun Lee. "Umbral Calculus and the Frobenius-Euler Polynomials." Abstract and Applied Analysis 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/871512.

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38

Gzyl, Henryk. "Canonical transformations, umbral calculus, and orthogonal theory." Journal of Mathematical Analysis and Applications 111, no. 2 (1985): 547–58. http://dx.doi.org/10.1016/0022-247x(85)90234-3.

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39

Ueno, Kazuo. "General power umbral calculus in several variables." Journal of Pure and Applied Algebra 59, no. 3 (1989): 299–308. http://dx.doi.org/10.1016/0022-4049(89)90100-x.

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40

Behr, Nicolas, Giuseppe Dattoli, Gérard Duchamp, and Silvia Penson. "Operational Methods in the Study of Sobolev-Jacobi Polynomials." Mathematics 7, no. 2 (2019): 124. http://dx.doi.org/10.3390/math7020124.

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Inspired by ideas from umbral calculus and based on the two types of integrals occurring in the defining equations for the gamma and the reciprocal gamma functions, respectively, we develop a multi-variate version of umbral calculus and of the so-called umbral image technique. Besides providing a class of new formulae for generalized hypergeometric functions and an implementation of series manipulations for computing lacunary generating functions, our main application of these techniques is the study of Sobolev-Jacobi polynomials. Motivated by applications to theoretical chemistry, we moreover

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41

Dattoli, Giuseppe, Silvia Licciardi, Bruna Germano, and Maria Renata Martinelli. "q-Functions and Distributions, Operational and Umbral Methods." Mathematics 9, no. 21 (2021): 2664. http://dx.doi.org/10.3390/math9212664.

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The use of non-standard calculus means have been proven to be extremely powerful for studying old and new properties of special functions and polynomials. These methods have helped to frame either elementary and special functions within the same logical context. Methods of Umbral and operational calculus have been embedded in a powerful and efficient analytical tool, which will be applied to the study of the properties of distributions such as Tsallis, Weibull and Student’s. We state that they can be viewed as standard Gaussian distributions and we take advantage of the relevant properties to

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42

Kim, T. "Identities involving Laguerre polynomials derived from umbral calculus." Russian Journal of Mathematical Physics 21, no. 1 (2014): 36–45. http://dx.doi.org/10.1134/s1061920814010038.

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43

Kim, T., and T. Mansour. "Umbral calculus associated with Frobenius-type Eulerian polynomials." Russian Journal of Mathematical Physics 21, no. 4 (2014): 484–93. http://dx.doi.org/10.1134/s1061920814040062.

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44

Kim, T., та D. S. Kim. "On λ-Bell polynomials associated with umbral calculus". Russian Journal of Mathematical Physics 24, № 1 (2017): 69–78. http://dx.doi.org/10.1134/s1061920817010058.

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45

Senato, D., and A. Venezia. "A set-theoretic interpretation of the umbral calculus." Computers & Mathematics with Applications 41, no. 9 (2001): 1109–24. http://dx.doi.org/10.1016/s0898-1221(01)00085-2.

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46

Saliani, Sandra, and Domenico Senato. "Compactly Supported Wavelets Through the Classical Umbral Calculus." Journal of Fourier Analysis and Applications 12, no. 1 (2006): 27–36. http://dx.doi.org/10.1007/s00041-005-4085-y.

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47

Wiseman, Gus. "Set maps, umbral calculus, and the chromatic polynomial." Discrete Mathematics 308, no. 16 (2008): 3551–64. http://dx.doi.org/10.1016/j.disc.2007.07.009.

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48

Andrews, George E. "Umbral Calculus, Bailey Chains, and Pentagonal Number Theorems." Journal of Combinatorial Theory, Series A 91, no. 1-2 (2000): 464–75. http://dx.doi.org/10.1006/jcta.2000.3111.

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49

Benyattou, Abdelkader, and Miloud Mihoubi. "Note on some sequences having periods that divide (formula)." Notes on Number Theory and Discrete Mathematics 28, no. 2 (2022): 234–39. http://dx.doi.org/10.7546/nntdm.2022.28.2.234-239.

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50

Licciardi, Silvia, Rosa Maria Pidatella, Marcello Artioli, and Giuseppe Dattoli. "Voigt Transform and Umbral Image." Mathematical and Computational Applications 25, no. 3 (2020): 49. http://dx.doi.org/10.3390/mca25030049.

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In this paper, we show that the use of methods of an operational nature, such as umbral calculus, allows achieving a double target: on one side, the study of the Voigt function, which plays a pivotal role in spectroscopic studies and in other applications, according to a new point of view, and on the other, the introduction of a Voigt transform and its possible use. Furthermore, by the same method, we point out that the Hermite and Laguerre functions, extension of the corresponding polynomials to negative and/or real indices, can be expressed through a definition in a straightforward and unifi

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