On a family of special numbers and polynomials associated with Apostol-type numbers and polynomials and combinatorial numbers

DOI10.2298/AADM180215016KMaRDI QIDQ5091840

Yilmaz Simsek, Irem Kucukoglu

Publication date: 27 July 2022

Published in: Applicable Analysis and Discrete Mathematics (Search for Journal in Brave)

zbMATH Keywords

generating functionsfunctional equationStirling numberscomputation algorithmApostol-type numbers and polynomials

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Bernoulli and Euler numbers and polynomials (11B68) Special sequences and polynomials (11B83)

Related Items (7)

New integral formulas and identities involving special numbers and functions derived from certain class of special combinatorial sums ⋮ Construction of general forms of ordinary generating functions for more families of numbers and multiple variables polynomials ⋮ 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 ⋮ A new class of generalized Fubini polynomials and their computational algorithms ⋮ Identities, inequalities for Boole-type polynomials: approach to generating functions and infinite series ⋮ Derivation of computational formulas for Changhee polynomials and their functional and differential equations

Cites Work

• Some generalizations of the Apostol-Genocchi polynomials and the Stirling numbers of the second kind
• A unified presentation of the generating functions of the generalized Bernoulli, Euler and Genocchi polynomials
• Applications on the Apostol-Daehee numbers and polynomials associated with special numbers, polynomials, and \(p\)-adic integrals
• Generating functions for generalized Stirling type numbers, array type polynomials, Eulerian type polynomials and their applications
• Partial differential equations for a new family of numbers and polynomials unifying the Apostol-type numbers and the Apostol-type polynomials
• Apostol-Euler polynomials of higher order and Gaussian hypergeometric functions
• Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials
• On the Lerch zeta function
• ON THE ANALOGS OF BERNOULLI AND EULER NUMBERS, RELATED IDENTITIES AND ZETA AND L-FUNCTIONS
• Construction of some new families of Apostol-type numbers and polynomials via Dirichlet character and p-adic q-integrals
• NOTE ON APOSTOL-DAEHEE POLYNOMIALS AND NUMBERS
• New families of special numbers for computing negative order Euler numbers and related numbers and polynomials
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