Formulas for Poisson-Charlier, Hermite, Milne-Thomson and other type polynomials by their generating functions and \(p\)-adic integral approach

DOI10.1007/s13398-018-0528-6zbMath1429.11046OpenAlexW2792593666WikidataQ130066580 ScholiaQ130066580MaRDI QIDQ2314639

Yilmaz Simsek

Publication date: 29 July 2019

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13398-018-0528-6

zbMATH Keywords

functional equationorthogonal polynomialsgenerating functionStirling numbersHermite polynomialsPoisson-Charlier polynomialsspecial functionsBernoulli numbers and polynomialsEuler numbers and polynomials\(p\)-adic integralspecial numbers and polynomialsMilne-Thomson Polynomials

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Bell and Stirling numbers (11B73) Bernoulli and Euler numbers and polynomials (11B68) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80)

Related Items

Identities and relations for Fubini type numbers and polynomials via generating functions and p-adic integral approach, Identities associated with Milne-Thomson type polynomials and special numbers, Poly-falling factorial sequences and poly-rising factorial sequences, New integral formulas and identities involving special numbers and functions derived from certain class of special combinatorial sums, On a class of generalized Humbert-Hermite polynomials via generalized Fibonacci polynomials, Formulae bringing to light from certain classes of numbers and polynomials, Explicit, determinantal, recursive formulas, and generating functions of generalized Humbert–Hermite polynomials via generalized Fibonacci polynomials, Sums of finite products of Legendre and Laguerre polynomials, Identities and relations for Hermite-based Milne-Thomson polynomials associated with Fibonacci and Chebyshev polynomials, Some certain classes of combinatorial numbers and polynomials attached to Dirichlet characters: their construction by \(p\)-adic integration and applications to probability distribution functions, Stirling-Dunkl numbers

Uses Software

• OPQ

Cites Work

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• Modification and unification of the Apostol-type numbers and polynomials and their applications
• Some array type polynomials associated with special numbers and polynomials
• Special functions related to Dedekind-type DC-sums and their applications
• Some generalizations of the Apostol-Genocchi polynomials and the Stirling numbers of the second kind
• \(q\)-Volkenborn integration
• Hermite polynomials and their applications associated with Bernoulli and Euler numbers
• Twisted \((h,q)\)-Bernoulli numbers and polynomials related to twisted \((h,q)\)-zeta function and \(L\)-function
• On the \(q\)-extension of Euler and Genocchi numbers
• Quadratures and integral transforms arising from generating functions
• Multidimensional extensions of the Bernoulli and Appell polynomials
• Generating functions for generalized Stirling type numbers, array type polynomials, Eulerian type polynomials and their applications
• Hermite base Bernoulli type polynomials on the umbral algebra
• The combinatorics of the Al-Salam-Chihara \(q\)-Charlier polynomials
• A New Nonparametric Estimation Method of the Variance in Heteroscedastic Model
• Complete sum of products of (h,q)-extension of Euler polynomials and numbers
• ON THE ANALOGS OF BERNOULLI AND EULER NUMBERS, RELATED IDENTITIES AND ZETA AND L-FUNCTIONS
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• Some formulas for the Bernoulli and Euler polynomials at rational arguments
• A new class of generalized polynomials