Generating functions for series involving higher powers of inverse binomial coefficients and their applications

DOI10.1002/mma.9199zbMath1528.33003OpenAlexW4327814618MaRDI QIDQ6178211

Yilmaz Simsek

Publication date: 18 January 2024

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.9199

zbMATH Keywords

algorithmsplinegenerating functionrecurrence relationsfinite sumsderivative operatorinverse binomial coefficientsspecial functions and special numbers

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15)

Cites Work

• Multiple binomial sums
• Some summation formulas involving harmonic numbers and generalized harmonic numbers
• Combinatorial identities and inverse binomial coefficients
• Eulerian numbers and polynomials of higher order
• Recurrences for alternating sums of powers of binomial coefficients
• Some new generalizations and applications of the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials
• On some degenerate differential and degenerate difference operators
• Binomial Eulerian polynomials for colored permutations
• Generating functions for finite sums involving higher powers of binomial coefficients: analysis of hypergeometric functions including new families of polynomials and numbers
• A generalized inverse binomial summation theorem and some hypergeometric transformation formulas
• On the Lerch zeta function
• New integral formulas and identities involving special numbers and functions derived from certain class of special combinatorial sums
• Permutations and sequences with repetitions by number of increases
• Construction of some new families of Apostol-type numbers and polynomials via Dirichlet character and p-adic q-integrals
• Computational formulas and identities for new classes of Hermite‐based Milne–Thomson type polynomials: Analysis of generating functions with Euler's formula
• New families of special numbers for computing negative order Euler numbers and related numbers and polynomials
• On an open problem of Simsek concerning the computation of a family of special numbers
• A Series transformation formula and related degenerate polynomials
• Generalized Exponential Euler Polynomials and Exponential Splines
• Explicit Formulas for Bernoulli Numbers
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