Relevant bibliographies by topics / Bernoulli numbers. Gamma functions

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Bernoulli numbers. Gamma functions'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Bernoulli numbers. Gamma functions"

1

Adegoke, Kunle. "Fibonacci series from power series." Notes on Number Theory and Discrete Mathematics 27, no. 3 (2021): 44–62. http://dx.doi.org/10.7546/nntdm.2021.27.3.44-62.

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We show how every power series gives rise to a Fibonacci series and a companion series involving Lucas numbers. For illustrative purposes, Fibonacci series arising from trigonometric functions, the gamma function and the digamma function are derived. Infinite series involving Fibonacci and Bernoulli numbers and Fibonacci and Euler numbers are also obtained.
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Zhu, Bao-Xuan. "The Monotonicity and Log-Behaviour of Some Functions Related to the Euler Gamma Function." Proceedings of the Edinburgh Mathematical Society 60, no. 2 (2016): 527–43. http://dx.doi.org/10.1017/s001309151600016x.

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AbstractThe aim of this paper is to develop analytic techniques to deal with the monotonicity of certain combinatorial sequences. On the one hand, a criterion for the monotonicity of the function is given, which is a continuous analogue of a result of Wang and Zhu. On the other hand, the log-behaviour of the functionsis considered, where ζ(x) and Γ(x) are the Riemann zeta function and the Euler Gamma function, respectively. Consequently, the strict log-concavities of the function θ(x) (a conjecture of Chen et al.) and for some combinatorial sequences (including the Bernoulli numbers, the tange
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Debnath, Lokenath, and Bicheng Yang. "Recent Developments of Hilbert-Type Discrete and Integral Inequalities with Applications." International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–29. http://dx.doi.org/10.1155/2012/871845.

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This paper deals with recent developments of Hilbert-type discrete and integral inequalities by introducing kernels, weight functions, and multiparameters. Included are numerous generalizations, extensions, and refinements of Hilbert-type inequalities involving many special functions such as beta, gamma, logarithm, trigonometric, hyper-bolic, Bernoulli's functions and Bernoulli's numbers, Euler's constant, zeta function, and hypergeometric functions with many applications. Special attention is given to many equivalent inequalities and to conditions under which the constant factors involved in
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Deeba, Elias Y., and Dennis M. Rodriguez. "Bernoulli numbers and trigonometric functions." International Journal of Mathematical Education in Science and Technology 21, no. 2 (1990): 275–82. http://dx.doi.org/10.1080/0020739900210214.

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Zhang, Wenpeng, and Xin Lin. "Identities involving trigonometric functions and Bernoulli numbers." Applied Mathematics and Computation 334 (October 2018): 288–94. http://dx.doi.org/10.1016/j.amc.2018.04.015.

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Noh, Hae-Young, Anne Kiremidjian, Luis Ceferino, and Emily So. "Bayesian Updating of Earthquake Vulnerability Functions with Application to Mortality Rates." Earthquake Spectra 33, no. 3 (2017): 1173–89. http://dx.doi.org/10.1193/081216eqs133m.

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Vulnerability functions often rely on data from expert opinion, post-earthquake investigations, or analytical simulations. Combining the information can be particularly challenging. In this paper, a Bayesian statistical framework is presented to combining disparate information. The framework is illustrated through application to earthquake mortality data obtained from the 2005 Pakistan earthquake and from PAGER. Three different models are tested including an exponential, a combination of Bernoulli and exponential and Bernoulli and gamma fit to model respectively zero and non-zero mortality rat
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KANEKO, MASANOBU, and HIROFUMI TSUMURA. "MULTI-POLY-BERNOULLI NUMBERS AND RELATED ZETA FUNCTIONS." Nagoya Mathematical Journal 232 (May 8, 2017): 19–54. http://dx.doi.org/10.1017/nmj.2017.16.

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We construct and study a certain zeta function which interpolates multi-poly-Bernoulli numbers at nonpositive integers and whose values at positive integers are linear combinations of multiple zeta values. This function can be regarded as the one to be paired up with the $\unicode[STIX]{x1D709}$-function defined by Arakawa and Kaneko. We show that both are closely related to the multiple zeta functions. Further we define multi-indexed poly-Bernoulli numbers, and generalize the duality formulas for poly-Bernoulli numbers by introducing more general zeta functions.
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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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Kim, T., S. H. Lee, Hyeon-Ho Han, and C. S. Ryoo. "On the Values of the Weighted -Zeta and -Functions." Discrete Dynamics in Nature and Society 2011 (2011): 1–7. http://dx.doi.org/10.1155/2011/476381.

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Recently, the modified -Bernoulli numbers and polynomials are introduced in (D. V. Dolgy et al., in press). These numbers are valuable to study the weighted -zeta and -functions. In this paper, we study the weighted -zeta functions and weighted -functions from the modified -Bernoulli numbers and polynomials with weight .
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Ma, Minyoung, and Dongkyu Lim. "A note on polyexponential and unipoly Bernoulli polynomials of the second kind." Open Mathematics 19, no. 1 (2021): 869–77. http://dx.doi.org/10.1515/math-2021-0052.

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Abstract In this paper, the authors study the poly-Bernoulli numbers of the second kind, which are defined by using polyexponential functions introduced by Kims. Also by using unipoly function, we study the unipoly Bernoulli numbers of the second kind, which are attached to an arithmetic function. We derive their explicit expressions and some identities involving poly-Bernoulli numbers of the second kind and unipoly Bernoulli numbers of the second kind.
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Dissertations / Theses on the topic "Bernoulli numbers. Gamma functions"

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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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Perkins, Rudolph Bronson. "On Special Values of Pellarin’s L-series." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1383827548.

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Books on the topic "Bernoulli numbers. Gamma functions"

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Arakawa, Tsuneo, Tomoyoshi Ibukiyama, and Masanobu Kaneko. Bernoulli Numbers and Zeta Functions. Springer Japan, 2014. http://dx.doi.org/10.1007/978-4-431-54919-2.

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author, Ibukiyama Tomoyoshi, Kaneko Masanobu author, and Zagier, Don, 1951- writer of supplementary textual content, eds. Bernoulli numbers and Zeta functions. Springer, 2014.

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Invitation to classical analysis. American Mathematical Society, 2012.

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Ibukiyama, Tomoyoshi, Masanobu Kaneko, Tsuneo Arakawa, and Don B. Zagier. Bernoulli Numbers and Zeta Functions. Springer, 2016.

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Ibukiyama, Tomoyoshi, Masanobu Kaneko, and Tsuneo Arakawa. Bernoulli Numbers and Zeta Functions. Springer, 2014.

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Book chapters on the topic "Bernoulli numbers. Gamma functions"

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Berndt, Bruce C. "Sums of Powers, Bernoulli Numbers, and the Gamma Function." In Ramanujan’s Notebooks. Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4612-1088-7_8.

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Ibukiyama, Tomoyoshi, and Masanobu Kaneko. "Bernoulli Numbers." In Bernoulli Numbers and Zeta Functions. Springer Japan, 2014. http://dx.doi.org/10.1007/978-4-431-54919-2_1.

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Ibukiyama, Tomoyoshi, and Masanobu Kaneko. "Poly-Bernoulli Numbers." In Bernoulli Numbers and Zeta Functions. Springer Japan, 2014. http://dx.doi.org/10.1007/978-4-431-54919-2_14.

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Ibukiyama, Tomoyoshi, and Masanobu Kaneko. "Generalized Bernoulli Numbers." In Bernoulli Numbers and Zeta Functions. Springer Japan, 2014. http://dx.doi.org/10.1007/978-4-431-54919-2_4.

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Ibukiyama, Tomoyoshi, and Masanobu Kaneko. "Stirling Numbers and Bernoulli Numbers." In Bernoulli Numbers and Zeta Functions. Springer Japan, 2014. http://dx.doi.org/10.1007/978-4-431-54919-2_2.

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Ibukiyama, Tomoyoshi, and Masanobu Kaneko. "Hurwitz Numbers." In Bernoulli Numbers and Zeta Functions. Springer Japan, 2014. http://dx.doi.org/10.1007/978-4-431-54919-2_12.

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Oldham, Keith B., Jan C. Myland, and Jerome Spanier. "The Bernoulli Numbers B n." In An Atlas of Functions. Springer US, 2008. http://dx.doi.org/10.1007/978-0-387-48807-3_5.

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Ibukiyama, Tomoyoshi, and Masanobu Kaneko. "Character Sums and Bernoulli Numbers." In Bernoulli Numbers and Zeta Functions. Springer Japan, 2014. http://dx.doi.org/10.1007/978-4-431-54919-2_8.

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Ibukiyama, Tomoyoshi, and Masanobu Kaneko. "Congruence Between Bernoulli Numbers and Class Numbers of Imaginary Quadratic Fields." In Bernoulli Numbers and Zeta Functions. Springer Japan, 2014. http://dx.doi.org/10.1007/978-4-431-54919-2_7.

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Ibukiyama, Tomoyoshi, and Masanobu Kaneko. "Class Number Formula and an Easy Zeta Function of the Space of Quadratic Forms." In Bernoulli Numbers and Zeta Functions. Springer Japan, 2014. http://dx.doi.org/10.1007/978-4-431-54919-2_10.

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Conference papers on the topic "Bernoulli numbers. Gamma functions"

1

Simsek, Yilmaz. "Multiple Interpolation Functions of Higher Order (h,q)‐Bernoulli Numbers." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2990969.

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