Generating functions for finite sums involving higher powers of binomial coefficients: analysis of hypergeometric functions including new families of polynomials and numbers

DOI10.1016/j.jmaa.2019.05.015zbMath1461.33003arXiv1901.02912OpenAlexW2909272291WikidataQ127893233 ScholiaQ127893233MaRDI QIDQ2315053

Yilmaz Simsek

Publication date: 31 July 2019

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.02912

zbMATH Keywords

generating functionsLegendre polynomialFranel numbersMirimanoff polynomial\(p\)-adic integralsBernoulli and Euler numbers and polynomials

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Factorials, binomial coefficients, combinatorial functions (05A10) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (16)

New integral formulas and identities involving special numbers and functions derived from certain class of special combinatorial sums ⋮ Computational identities for extensions of some families of special numbers and polynomials ⋮ On the generating functions and special functions associated with superoscillations ⋮ Explicit computations of some spectral invariants of compact symmetric spaces of rank one ⋮ Some identities of degenerate harmonic and degenerate hyperharmonic numbers arising from umbral calculus ⋮ Computational and implementational analysis of generating functions for higher order combinatorial numbers and polynomials attached to Dirichlet characters ⋮ Derivation of computational formulas for certain class of finite sums: Approach to generating functions arising from p$$ p $$‐adic integrals and special functions ⋮ Generating functions for generalization Simsek numbers and their applications ⋮ Recurrence relations, associated formulas, and combinatorial sums for some parametrically generalized polynomials arising from an analysis of the Laplace transform and generating functions ⋮ Generating functions for series involving higher powers of inverse binomial coefficients and their applications ⋮ Analysis of Apostol-Type Numbers and Polynomials with Their Approximations and Asymptotic Behavior ⋮ New classes of recurrence relations involving hyperbolic functions, special numbers and polynomials ⋮ Derivation of computational formulas for Changhee polynomials and their functional and differential equations ⋮ An affirmative answer to two questions concerning special case of Simsek numbers and open problems ⋮ Some certain classes of combinatorial numbers and polynomials attached to Dirichlet characters: their construction by \(p\)-adic integration and applications to probability distribution functions ⋮ Unnamed Item

Uses Software

• SumTools

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