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Displaying 21 – 40 of 106

Asymptotic analysis and special values of generalised multiple zeta functions

M. Zakrzewski (2012)

Banach Center Publications

This is an expository article, based on the talk with the same title, given at the 2011 FASDE II Conference in Będlewo, Poland. In the introduction we define Multiple Zeta Values and certain historical remarks are given. Then we present several results on Multiple Zeta Values and, in particular, we introduce certain meromorphic differential equations associated to their generating function. Finally, we make some conclusive remarks on generalisations of Multiple Zeta Values as well as the meromorphic...

Asymptotic expansions for ratios of products of gamma functions.

Bühring, Wolfgang (2003)

International Journal of Mathematics and Mathematical Sciences

Binomial sums via Bailey's cubic transformation

Wenchang Chu (2023)

Czechoslovak Mathematical Journal

By employing one of the cubic transformations (due to W. N. Bailey (1928)) for the $_{3} F_{2} (x)$ -series, we examine a class of $_{3} F_{2} (4)$ -series. Several closed formulae are established by means of differentiation, integration and contiguous relations. As applications, some remarkable binomial sums are explicitly evaluated, including one proposed recently as an open problem.

Certain Properties of Fractional Calculus Operators Associated with Generalized Mittag-Leffler Function

Saxena, R. K., Saigo, Megumi (2005)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 26A33, 33E12, 33C20.It has been shown that the fractional integration and differentiation operators transform such functions with power multipliers into the functions of the same form. Some of the results given earlier by Kilbas and Saigo follow as special cases.

Certain results involving generalized hypergeometric polynomials

R. S. Dahiya (1971)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

Computing Gauss-Manin systems for complete intersection singularities $S_{μ}$ .

Aleksandrov, A.G., Tanabé, S. (1996)

Georgian Mathematical Journal

Contiguous extensions of Dixon's theorem on the sum of a $_{3} F_{2}$ .

Choi, Junesang (2010)

Journal of Inequalities and Applications [electronic only]

Démonstration «automatique» d'identités et fonctions hypergéométriques

Pierre Cartier (1991/1992)

Séminaire Bourbaki

Derangements and applications.

Hassani, Mehdi (2003)

Journal of Integer Sequences [electronic only]

Derivatives of Catalan related sums.

Sofo, Anthony (2009)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Determinant identities and a generalization of the number of totally symmetric self-complementary plane partitions.

Krattenthaler, C. (1997)

The Electronic Journal of Combinatorics [electronic only]

Determinant inequalities for sieved ultraspherical polynomials.

Bustoz, J., Pyung, I.S. (2001)

International Journal of Mathematics and Mathematical Sciences

Dixon's formula and identities involving harmonic numbers.

Wang, Xiaoxia, Li, Mei (2011)

Journal of Integer Sequences [electronic only]

Duplicate inverse series relations and hypergeometric evaluations with $z = 1 / 4$

Wenchang Chu (2002)

Bollettino dell'Unione Matematica Italiana

The Gould-Hsu (1973) inverse series relations have been systematically applied to the research of hypergeometric identities. Their duplicate version is established and used to demonstrate several terminating ${}_{3}F_{2} [1 / 4]$ -summation formulas. Further hypergeometric evaluations with the same variable are obtained through recurrence relations.

Experimental determination of Apéry-like identities for $ζ (2 n + 2)$ .

Bailey, David H., Borwein, Jonathan M., Bradley, David M. (2006)

Experimental Mathematics

Extended Bell and Stirling numbers from hypergeometric exponentiation.

Sixdeniers, J.-M., Penson, K.A., Solomon, A.I. (2001)

Journal of Integer Sequences [electronic only]

Extensions of Bailey's transform and applications.

Joshi, C.M., Vyas, Yashoverdhan (2005)

International Journal of Mathematics and Mathematical Sciences

Extensions of certain classical summation theorems for the series $_{2} F_{1}$ , $_{3} F_{2}$ and with applications in Ramanujan's summations.

Kim, Yong Sup, Rakha, Medhat A., Rathie, Arjun K. (2010)

International Journal of Mathematics and Mathematical Sciences

First hitting time of the boundary of the Weyl chamber by radial Dunkl processes.

Demni, Nizar (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Four-term recurrence relations for hypergeometric functions of the second order. II.

Harold Exton (1998)

Collectanea Mathematica

The recent work on four-term recurrence relations for the second order functions of hypergeometric type undertaken by the author is developed from a slightly different point of view also using generating functions. The direction of future prospects is indicated.

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