Power Series with Inverse Binomial Coefficients and Harmonic Numbers

Boyadzhiev, Khristo N.

doi:10.1515/tmmp-2017-0027

.blurhash-client-img { display: none !important; }

Power Series with Inverse Binomial Coefficients and Harmonic Numbers

Tatra Mountains Mathematical Publications

Volume 70 (2017): Issue 1 (September 2017)

By: Khristo N. Boyadzhiev

Open Access

|Mar 2018

Abstract

In this note we compute the generating function for the numbers terms of elementary functions and dilogarithms.

References

[1] APÉRY, R.: Irrationalit de ζ(2) et ζ(3). In: Luminy Conference on Arithmetic, Asterique, 61 (1979), pp. 11-13.
Search in Google Scholar Back to article
[2] BOYADZHIEV, K. N.: Series transformations formulas of Euler type, Hadamard product of series, and harmonic number identities, Indian J. Pure and Appl. Math., 42 (2011), no. 5, 371-387; also at [arXiv:0912.5376v1 [math.NT]].
Search in Google Scholar Back to article
[3] Series with central binomial coefficients, Catalan numbers, and harmonic numbers, J. Int. Seq. 15 (2012), no. 1, Article 12.1.7., 11 pages.
Search in Google Scholar Back to article
[4] DAVYDYCHEV, A. I.-KALMYKOV, M. Y.: Massive Feynman diagrams and inverse binomial sums, Nuclear Phys. B 699, (2004), no. 1-2, 3-64 [arxiv.org/abs/hep-th/0303162].
Search in Google Scholar Back to article
[5] GENČEV, M.: Binomial sums involving harmonic numbers, Math. Slovaca 61, no.2 (2011), 215-226.10.2478/s12175-011-0006-5
Search in Google Scholar Back to article
[6] GLASSER, M. L.: A Generalized Ap´ery Series, J. Int. Seq. 15 (2012), no. 4, Article 12.4.3. 7. pp.
Search in Google Scholar Back to article
[7] KALMYKOV, M. Y.-VERETIN, O.: Single-scale diagrams and multiple binomial sums, Phys. Lett. B483 (2000), no. 1-3, 315-323, 10.1016/S0370-2693(00)00574-8
Search in Google Scholar Back to article
[8] KALMYKOV, M. Y.- WARD, B. F. L.-YOST, S. A.: Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order ε-expansion of generalized hypergeometric functions with one half-integer value of parameter, J. High Energy Phys. JHEP 10 (2007), [arxiv.org/pdf/0707.3654.pdf ].10.1088/1126-6708/2007/10/048
Search in Google Scholar Back to article
[9] LEHMER, D. H.: Interesting series involving the central binomial coefficient, Amer.Math. Monthly, 92 (1985), no. 7, 449-457.
Search in Google Scholar Back to article
[10] SPRUGNOLI, R.: Sums of reciprocals of the central binomial coefficients, Integers 6 (2006), #A 27.
Search in Google Scholar Back to article

DOI: https://doi.org/10.1515/tmmp-2017-0027 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195

Journal RSS Feed

Language: English

Page range: 199 - 206

Submitted on: Jan 17, 2017

Published on: Mar 23, 2018

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

05A15,

11B05

Related subjects:

Mathematics,

General mathematics

© 2018 Khristo N. Boyadzhiev, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Previous article Volume 70 (2017): Issue 1 (September 2017)Next article