Formulas for \(p\)-adic \(q\)-integrals including falling-rising factorials, combinatorial sums and special numbers

DOI10.1007/S13398-024-01592-1zbMATH Open1543.11106MaRDI QIDQ6552629

Yilmaz Simsek

Publication date: 10 June 2024

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

zbMATH Keywords

generating functionStirling numbersLah numbersharmonic numbersBernoulli numbers and polynomialsEuler numbers and polynomialsFubini numbers\(p\)-adic \(q\)-integralscombinatorial numbers and sums

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial identities, bijective combinatorics (05A19) Bernoulli and Euler numbers and polynomials (11B68) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Hurwitz and Lerch zeta functions (11M35)

Cites Work

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• Some array type polynomials associated with special numbers and polynomials
• Several identities involving the falling and rising factorials and the Cauchy, Lah, and Stirling numbers
• Some generalizations of the Apostol-Genocchi polynomials and the Stirling numbers of the second kind
• \(q\)-Volkenborn integration
• Lah numbers, Laguerre polynomials of order negative one, and the \(n\)th derivative of \(\exp(1/x)\)
• A multiplication theorem for the Lerch zeta function and explicit representations of the Bernoulli and Euler polynomials
• \(q\)-Bernoulli numbers and polynomials associated with multiple \(q\)-zeta functions and basic \(L\)-series
• On the analogs of Euler numbers and polynomials associated with \(p\)-adic \(q\)-integral on \(\mathbb Z_{p}\) at \(q= - 1\)
• New families of special numbers and polynomials arising from applications of \( p\)-adic \( q\)-integrals
• Identities associated with generalized Stirling type numbers and Eulerian type polynomials
• Barnes' multiple Frobenius-Euler and poly-Bernoulli mixed-type polynomials
• Generating functions for generalized Stirling type numbers, array type polynomials, Eulerian type polynomials and their applications
• An invariant \(p\)-adic \(q\)-integral on \(\mathbb Z _p\)
• On the Lerch zeta function
• A Course in Enumeration
• ON THE ANALOGS OF BERNOULLI AND EULER NUMBERS, RELATED IDENTITIES AND ZETA AND L-FUNCTIONS
• Falling Factorials, Generating Functions, and Conjoint Ranking Tables
• A NEW FAMILY OF FUBINI TYPE NUMBERS AND POLYNOMIALS ASSOCIATED WITH APOSTOL-BERNOULLI NUMBERS AND POLYNOMIALS
• Combinatorial Methods in Discrete Distributions
• Close Encounters with the Stirling Numbers of the Second Kind
• Analysis of the p-adic q-Volkenborn integrals: An approach to generalized Apostol-type special numbers and polynomials and their applications
• A note on Boole polynomials
• ANALYTIC PROPERTIES OF THE q-VOLKENBORN INTEGRAL ON THE RING OF p-ADIC INTEGERS

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