Integral and series representations of q-polynomials and functions: Part I

DOI10.1142/S0219530517500129zbMath1387.33022arXiv1604.08441OpenAlexW2963117169MaRDI QIDQ4602845

Ruiming Zhang, Mourad E. H. Ismail

Publication date: 7 February 2018

Published in: Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.08441

zbMATH Keywords

Fourier transformsMellin transformsStieltjes-Wigert polynomialsbasic hypergeometric series\(q\)-Bessel functionsmultiplication formulas\(q\)-Laguerre polynomialsRamanujan functionconnection relations\(q\)-exponential functionsbilateral hypergeometric series\(q^{- 1}\)-Hermite polynomials

Mathematics Subject Classification ID

Integral transforms of special functions (44A20) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Basic hypergeometric integrals and functions defined by them (33D60)

Related Items (7)

Integral and series representations of q-polynomials and functions: Part III theta, Ramanujan and q-Bessel functions ⋮ Asymptotics for some \(q\)-hypergeometric polynomials ⋮ Statistical \((C,1)(E,\mu )\)-summability and associated fuzzy approximation theorems with statistical fuzzy rates ⋮ 𝑞-Bessel functions and Rogers-Ramanujan type identities ⋮ On Approximation of Signals in the Weighted Zygmund Class via $$(E,1)(\overline{N},p_{n})$$ Summability Means of Conjugate Fourier Series ⋮ Solutions of the Al-Salam–Chihara and allied moment problems ⋮ Integral and series representations of 𝑞-polynomials and functions: Part II Schur polynomials and the Rogers-Ramanujan identities

Cites Work

• Zeros of entire functions and a problem of Ramanujan
• \(q\)-Taylor and interpolation series for Jackson \(q\)-difference operators
• The zeros of basic Bessel functions, the functions J(nu+ax)(x), and associated orthogonal polynomials
• Diagonalization of certain integral operators
• The \(q\)-Laguerre polynomials and related moment problems
• The moment problem associated with the \(q\)-Laguerre polynomials
• The moment problem associated with the Stieltjes-Wigert polynomials
• Chaotic and periodic asymptotics for q-orthogonal polynomials
• SCALED ASYMPTOTICS FOR SOME q-SERIES
• q-Hermite Polynomials, Biorthogonal Rational Functions, and q-Beta Integrals
• 𝑞-Bessel functions and Rogers-Ramanujan type identities
• Integral and series representations of 𝑞-polynomials and functions: Part II Schur polynomials and the Rogers-Ramanujan identities
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