Construction of some new families of Apostol-type numbers and polynomials via Dirichlet character and p-adic q-integrals

DOI10.3906/mat-1703-114zbMath1438.11056OpenAlexW2791404527WikidataQ130069088 ScholiaQ130069088MaRDI QIDQ4634117

Yilmaz Simsek

Publication date: 7 May 2019

Published in: TURKISH JOURNAL OF MATHEMATICS (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3906/mat-1703-114

zbMATH Keywords

generating functionStirling numbersDirichlet charactergeneralized Bernoulli numbers and polynomialsgeneralized Euler numbers and polynomials\(p\)-adic Volkenborn integralDaehee numbers and polynomialsApostol-Bernoulli and Apostol-Euler numbers and polynomials

Mathematics Subject Classification ID

Bell and Stirling numbers (11B73) Bernoulli and Euler numbers and polynomials (11B68) Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80)

Related Items (28)

Unnamed Item ⋮ Implementation of computation formulas for certain classes of Apostol-type polynomials and some properties associated with these polynomials ⋮ Partial derivative formulas and identities involving 2-variable Simsek polynomials ⋮ On a family of special numbers and polynomials associated with Apostol-type numbers and polynomials and combinatorial numbers ⋮ Computational identities for extensions of some families of special numbers and polynomials ⋮ A special approach to derive new formulas for some special numbers and polynomials ⋮ New classes of Catalan-type numbers and polynomials with their applications related to p-adic integrals and computational algorithms ⋮ Construction of general forms of ordinary generating functions for more families of numbers and multiple variables polynomials ⋮ Modification exponential Euler type splines derived from Apostol-Euler numbers and polynomials of complex order ⋮ Computational and implementational analysis of generating functions for higher order combinatorial numbers and polynomials attached to Dirichlet characters ⋮ 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 ⋮ A note on polynomial expressions for sums of power of integers multiplied by exponential terms ⋮ Properties and graphical representations of the 2-variable form of the Simsek polynomials ⋮ Special numbers and polynomials including their generating functions in umbral analysis methods ⋮ Generating functions for finite sums involving higher powers of binomial coefficients: analysis of hypergeometric functions including new families of polynomials and numbers ⋮ A note on modified degenerate \(q\)-Daehee polynomials and numbers ⋮ 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 ⋮ Differential equations associated with degenerate Changhee numbers of the second kind ⋮ A new family of combinatorial numbers and polynomials associated with peters numbers and polynomials ⋮ Applications of Apostol-type numbers and polynomials: approach to techniques of computation algorithms in approximation and interpolation functions ⋮ Some certain classes of combinatorial numbers and polynomials attached to Dirichlet characters: their construction by \(p\)-adic integration and applications to probability distribution functions ⋮ On generating functions for Boole type polynomials and numbers of higher order and their applications ⋮ Some new identities and formulas for higher-order combinatorial-type numbers and polynomials ⋮ On Boole-type combinatorial numbers and polynomials ⋮ Matrix representations for a certain class of combinatorial numbers associated with Bernstein basis functions and cyclic derangements and their probabilistic and asymptotic analyses ⋮ Computation of k-ary Lyndon words using generating functions and their differential equations

Cites Work

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