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Relevant bibliographies by topics / Bernoulli polynomials

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Academic literature on the topic 'Bernoulli polynomials'

Author: Grafiati

Published: 4 June 2021

Last updated: 31 July 2024

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Journal articles on the topic "Bernoulli polynomials"

1

Cao, Jian, José Luis López-Bonilla, and Feng Qi. "Three identities and a determinantal formula for differences between Bernoulli polynomials and numbers." Electronic Research Archive 32, no. 1 (2023): 224–40. http://dx.doi.org/10.3934/era.2024011.

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<abstract><p>In the paper, the authors simply review recent results of inequalities, monotonicity, signs of determinants, determinantal formulas, closed-form expressions, and identities of the Bernoulli numbers and polynomials, establish an identity involving the differences between the Bernoulli polynomials and the Bernoulli numbers, present two identities among the differences between the Bernoulli polynomials and the Bernoulli numbers in terms of a determinant and a partial Bell polynomial, and derive a determinantal formula of the differences between the Bernoulli polynomials a

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2

Corcino, Roberto Bagsarsa, and Cristina Corcino. "Fourier Series for Bernoulli-Type Polynomials, Euler-Type Polynomials and Genocchi-Type Polynomials of Integer Order." European Journal of Pure and Applied Mathematics 15, no. 4 (2022): 1662–82. http://dx.doi.org/10.29020/nybg.ejpam.v15i4.4507.

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Parameters a, b, c, and α are introduced to form the Bernoulli-type, Euler-type and Genocchi-type polynomilas where α is the order of the polynomial and is a positive integer. Ana- lytic methods are used here to obtain the Fourier series for these polynomials.

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3

Navas, Luis M., Francisco J. Ruiz, and Juan L. Varona. "Old and New Identities for Bernoulli Polynomials via Fourier Series." International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/129126.

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The Bernoulli polynomialsBkrestricted to[0,1)and extended by periodicity haventh sine and cosine Fourier coefficients of the formCk/nk. In general, the Fourier coefficients of any polynomial restricted to[0,1)are linear combinations of terms of the form1/nk. If we can make this linear combination explicit for a specific family of polynomials, then by uniqueness of Fourier series, we get a relation between the given family and the Bernoulli polynomials. Using this idea, we give new and simpler proofs of some known identities involving Bernoulli, Euler, and Legendre polynomials. The method can a

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4

Luo, Qiu-Ming, Bai-Ni Guo, Feng Qi, and Lokenath Debnath. "Generalizations of Bernoulli numbers and polynomials." International Journal of Mathematics and Mathematical Sciences 2003, no. 59 (2003): 3769–76. http://dx.doi.org/10.1155/s0161171203112070.

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The concepts of Bernoulli numbersBn, Bernoulli polynomialsBn(x), and the generalized Bernoulli numbersBn(a,b)are generalized to the oneBn(x;a,b,c)which is called the generalized Bernoulli polynomials depending on three positive real parameters. Numerous properties of these polynomials and some relationships betweenBn,Bn(x),Bn(a,b), andBn(x;a,b,c)are established.

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5

Bayad, Abdelmejid, and Yilmaz Simsek. "On Generating Functions for Parametrically Generalized Polynomials Involving Combinatorial, Bernoulli and Euler Polynomials and Numbers." Symmetry 14, no. 4 (2022): 654. http://dx.doi.org/10.3390/sym14040654.

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The aim of this paper is to give generating functions for parametrically generalized polynomials that are related to the combinatorial numbers, the Bernoulli polynomials and numbers, the Euler polynomials and numbers, the cosine-Bernoulli polynomials, the sine-Bernoulli polynomials, the cosine-Euler polynomials, and the sine-Euler polynomials. We investigate some properties of these generating functions. By applying Euler’s formula to these generating functions, we derive many new and interesting formulas and relations related to these special polynomials and numbers mentioned as above. Some s

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6

Khan, Subuhi, and Mumtaz Riyasat. "Differential and integral equations for the 2-iterated Bernoulli, 2-iterated Euler and Bernoulli–Euler polynomials." Georgian Mathematical Journal 27, no. 3 (2020): 375–89. http://dx.doi.org/10.1515/gmj-2018-0062.

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AbstractThe main goal of this article is to derive differential and associated integral equations for some 2-iterated and mixed type special polynomial families. By using the factorization method, the recurrence relations and differential equations are derived for the 2-iterated Bernoulli, 2-iterated Euler and Bernoulli–Euler polynomials. The Volterra integral equations for these polynomial families are also established. The graphical representation of these 2-iterated and mixed polynomials is presented. The zeros of these polynomials are investigated for certain values of the index n using nu

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7

Bretti, Gabriella, Pierpaolo Natalini, and Paolo E. Ricci. "Generalizations of the Bernoulli and Appell polynomials." Abstract and Applied Analysis 2004, no. 7 (2004): 613–23. http://dx.doi.org/10.1155/s1085337504306263.

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We first introduce a generalization of the Bernoulli polynomials, and consequently of the Bernoulli numbers, starting from suitable generating functions related to a class of Mittag-Leffler functions. Furthermore, multidimensional extensions of the Bernoulli and Appell polynomials are derived generalizing the relevant generating functions, and using the Hermite-Kampé de Fériet (or Gould-Hopper) polynomials. The main properties of these polynomial sets are shown. In particular, the differential equations can be constructed by means of the factorization method.

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8

Urieles, Alejandro, María José Ortega, William Ramírez, and Samuel Vega. "New results on the q-generalized Bernoulli polynomials of level m." Demonstratio Mathematica 52, no. 1 (2019): 511–22. http://dx.doi.org/10.1515/dema-2019-0039.

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AbstractThis paper aims to show new algebraic properties from the q-generalized Bernoulli polynomials B_n^{[m - 1]}(x;q) of level m, as well as some others identities which connect this polynomial class with the q-generalized Bernoulli polynomials of level m, as well as the q-gamma function, and the q-Stirling numbers of the second kind and the q-Bernstein polynomials.

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9

HASSEN, ABDUL, and HIEU D. NGUYEN. "HYPERGEOMETRIC BERNOULLI POLYNOMIALS AND APPELL SEQUENCES." International Journal of Number Theory 04, no. 05 (2008): 767–74. http://dx.doi.org/10.1142/s1793042108001754.

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There are two analytic approaches to Bernoulli polynomials Bn(x): either by way of the generating function zexz/(ez - 1) = ∑ Bn(x)zn/n! or as an Appell sequence with zero mean. In this article, we discuss a generalization of Bernoulli polynomials defined by the generating function zN exz/(ez - TN-1(z)), where TN(z) denotes the Nth Maclaurin polynomial of ez, and establish an equivalent definition in terms of Appell sequences with zero moments in complete analogy to their classical counterpart. The zero-moment condition is further shown to generalize to Bernoulli polynomials generated by the co

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10

Bayad, Abdelmejid, and Matthias Beck. "Relations for Bernoulli–Barnes numbers and Barnes zeta functions." International Journal of Number Theory 10, no. 05 (2014): 1321–35. http://dx.doi.org/10.1142/s1793042114500298.

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The Barnes ζ-function is [Formula: see text] defined for [Formula: see text], Re (x) > 0, and Re (z) > n and continued meromorphically to ℂ. Specialized at negative integers -k, the Barnes ζ-function gives [Formula: see text] where Bk(x; a) is a Bernoulli–Barnes polynomial, which can be also defined through a generating function that has a slightly more general form than that for Bernoulli polynomials. Specializing Bk(0; a) gives the Bernoulli–Barnes numbers. We exhibit relations among Barnes ζ-functions, Bernoulli–Barnes numbers and polynomials, which generalize various identities of Ag

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Dissertations / Theses on the topic "Bernoulli polynomials"

1

Komori, Yasushi, Kohji Matsumoto, and Hirofumi Tsumura. "Zeta and L-functions and Bernoulli polynomials of root systems." Japan Academy, 2008. http://hdl.handle.net/2237/13843.

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2

Yingst, Andrew Q. "A Characterization of Homeomorphic Bernoulli Trial Measures." Thesis, University of North Texas, 2006. https://digital.library.unt.edu/ark:/67531/metadc5331/.

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We give conditions which, given two Bernoulli trial measures, determine whether there exists a homeomorphism of Cantor space which sends one measure to the other, answering a question of Oxtoby. We then provide examples, relating these results to the notions of good and refinable measures on Cantor space.

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3

Mirkoski, Maikon Luiz. "Números e polinômios de Bernoulli." Universidade Estadual de Ponta Grossa, 2018. http://tede2.uepg.br/jspui/handle/prefix/2699.

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Submitted by Angela Maria de Oliveira (amolivei@uepg.br) on 2018-11-29T18:07:06Z No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Maikon Luiz.pdf: 959643 bytes, checksum: aaf472f5b8a9a29532793d01234788a9 (MD5)<br>Made available in DSpace on 2018-11-29T18:07:06Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Maikon Luiz.pdf: 959643 bytes, checksum: aaf472f5b8a9a29532793d01234788a9 (MD5) Previous issue date: 2018-10-19<br>Neste trabalho,estudamos os números e os polinomios de Bernoulli,bem como a

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Tsumura, Hirofumi, Kohji Matsumoto, and Yasushi Komori. "A survey on the theory of multiple Bernoulli polynomials and multiple L-functions of root systems." Research Institute for Mathematical Sciences , Kyoto University, 2011. http://hdl.handle.net/2237/20334.

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Tsumura, Hirofumi, Kohji Matsumoto, and Yasushi Komori. "On Witten multiple zeta-functions associated with semisimple Lie algebras II." 日本数学会, 2010. http://hdl.handle.net/2237/20065.

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6

Kondo, Pedro Kiochi. "CÁLCULO FINITO: DEMONSTRAÇÕES E APLICAÇÕES." UNIVERSIDADE ESTADUAL DE PONTA GROSSA, 2014. http://tede2.uepg.br/jspui/handle/prefix/1528.

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Made available in DSpace on 2017-07-21T20:56:33Z (GMT). No. of bitstreams: 1 Pedro Kiochi Kondo.pdf: 1227541 bytes, checksum: daffb8a8bc299356bce288603753944c (MD5) Previous issue date: 2014-09-30<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>In this work some topics of the Discrete or Finite Calculus are developed. In particular, we study difference operators, factorial powers, Stirling numbers of the first and second type, the Newton’s formula of differences, the fundamental theorem of the Finite Calculus, the summation process, and the Bernoulli numbers and Bernoulli p

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7

Hsien, Lee Chung, and 李俊賢. "Identities Among Sums of Certain Trigonometric Series and Bernoulli Polynomials." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/61470431512152470704.

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碩士<br>國立中正大學<br>數學研究所<br>90<br>In this paper , we will derive some identities among the trigonometric series and Bernoulli polynomials . For getting these results , We consider the rational function F(T) and We can get the values of zeta function at negative integers from two ways . At last , by comparing the results , we can get these identities .

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Books on the topic "Bernoulli polynomials"

1

Dilcher, Karl. Zeros of Bernoulli, generalized Bernoulli, and Euler polynomials. American Mathematical Society, 1988.

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Shigeru, Kanemitsu, Tsukada Haruo 1961-, and Kanemitsu Shigeru, eds. Vistas of special functions II. World Scientific, 2010.

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Kanemitsu, Shigeru. Vistas of special functions. World Scientific, 2007.

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Tsukada, Haruo. Vistas of Special Functions II. World Scientific Publishing Co Pte Ltd, 2009.

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5

Marcus, Brian, and Selim Tuncel. Resolving Markov Chains Onto Bernoulli Shifts Via Positive Polynomials (Memoirs of the American Mathematical Society). American Mathematical Society, 2001.

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6

Bartolomeo, Jerry. Uniform stabilization of the Euler-Bernoulli equation with active Dirichlet and non-active Neumann boundary feedback controls. 1988.

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Vistas of Special Functions. World Scientific Publishing Company, 2007.

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Tsukada, Haruo. Vistas of Special Functions. World Scientific Publishing Co Pte Ltd, 2007.

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Tsukada, Haruo. Vistas of Special Functions. World Scientific Publishing Co Pte Ltd, 2007.

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Book chapters on the topic "Bernoulli polynomials"

1

Moll, Victor. "Bernoulli polynomials." In The Student Mathematical Library. American Mathematical Society, 2012. http://dx.doi.org/10.1090/stml/065/13.

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2

Brass, Helmut, and Knut Petras. "Bernoulli polynomials." In Quadrature Theory. American Mathematical Society, 2011. http://dx.doi.org/10.1090/surv/178/12.

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3

Kac, Victor, and Pokman Cheung. "Bernoulli Polynomials and Bernoulli Numbers." In Quantum Calculus. Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4613-0071-7_23.

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4

Viola, Carlo. "Bernoulli Numbers and Polynomials." In UNITEXT. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-41345-7_4.

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5

Schweizer, Wolfgang. "Bernoulli and Euler Polynomials." In Special Functions in Physics with MATLAB. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-64232-7_19.

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6

Sivaraman, R. "Bernoulli Polynomials and Ramanujan Summation." In Advances in Intelligent Systems and Computing. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-33-4389-4_44.

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7

Oldham, Keith B., Jan C. Myland, and Jerome Spanier. "The Bernoulli Polynomials B n (x)." In An Atlas of Functions. Springer US, 2008. http://dx.doi.org/10.1007/978-0-387-48807-3_20.

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8

Cholewinski, Frank M. "16. Bernoulli Type Polynomials and Numbers." In Contemporary Mathematics. American Mathematical Society, 1988. http://dx.doi.org/10.1090/conm/075/16.

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Cesarano, Clemente, and Alexandra Parmentier. "A Note on Hermite-Bernoulli Polynomials." In SEMA SIMAI Springer Series. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69236-0_6.

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Simsek, Yilmaz. "Families of Twisted Bernoulli Numbers, Twisted Bernoulli Polynomials, and Their Applications." In Analytic Number Theory, Approximation Theory, and Special Functions. Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4939-0258-3_6.

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Conference papers on the topic "Bernoulli polynomials"

1

KURT, BURAK, and VELİ KURT. "HERMITE-BERNOULLI 2D POLYNOMIALS." In Proceedings of the 13th Regional Conference. World Scientific Publishing Company, 2012. http://dx.doi.org/10.1142/9789814417532_0004.

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Kurt, Burak, Yilmaz Simsek, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Frobenious-Euler Type Polynomials Related to Hermite-Bernoulli Polynomials." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636743.

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Açíkgöz, Mehmet, Serkan Araci, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "The Relations Between Bernoulli, Bernstein and Euler Polynomials." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3497857.

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4

Bicer, Kubra Erdem, and Salih Yalcinbas. "Numerical solutions for Helmholtz equations using Bernoulli polynomials." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992470.

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"Lacunary recurrence relations for Bernoulli and Euler polynomials." In Уфимская осенняя математическая школа - 2022. Т.1. Baskir State University, 2022. http://dx.doi.org/10.33184/mnkuomsh1t-2022-09-28.17.

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Cetin, Yagmur, and Yilmaz Simsek. "Formulas for a new class of polynomials containing Bernoulli, Euler and Genocchi polynomials." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2021. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0162337.

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VERGNE, MICHÈLE. "LECTURE 1 RESIDUE FORMULAE FOR BERNOULLI POLYNOMIALS AND VERLINDE SUMS." In Proceedings of the Tenth General Meeting. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704276_0013.

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Bokhari, Ahmed, and Fethi Bin Muhammad Belgacem. "Applications of the Sumudu transform to Bernoulli numbers and polynomials." In ICNPAA 2016 WORLD CONGRESS: 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences. Author(s), 2017. http://dx.doi.org/10.1063/1.4972621.

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Agyuz, Erkan. "A note on Bernoulli and Euler type numbers and polynomials." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: ICNAAM2022. AIP Publishing, 2024. http://dx.doi.org/10.1063/5.0210609.

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Aygunes, Aykut Ahmet. "Convolution formulae related to special case of Euler and Bernoulli polynomials." In CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2019 (CEST). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5114090.

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