Zeros of entire functions and a problem of Ramanujan

DOI10.1016/j.aim.2006.05.007zbMath1107.33018OpenAlexW1977989145MaRDI QIDQ864575

Changgui Zhang, Mourad E. H. Ismail

Publication date: 12 February 2007

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2006.05.007

zbMATH Keywords

asymptoticszerosrecurrence relationsStieltjes-Wigert polynomials\(q\)-Bessel functions\(q\)-Laguerre polynomials\(q\)-Airy functionsRamanujan's entire function

Mathematics Subject Classification ID

Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Elliptic functions and integrals (33E05)

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Cites Work

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• Orthogonal polynomials associated with the Rogers-Ramanujan continued fraction
• Ramanujan's ``Lost notebook. VIII: The entire Rogers-Ramanujan function
• Ramanujan's ``lost notebook. IX: The partial theta function as an entire function
• Uniform asymptotics of the Stieltjes-Wigert polynomials via the Riemann-Hilbert approach
• The q-analogue of the Laguerre polynomials
• The zeros of basic Bessel functions, the functions J(nu+ax)(x), and associated orthogonal polynomials
• About Jackson \(q\)-Bessel functions
• The moment problem associated with the Stieltjes-Wigert polynomials
• The special functions and their approximations. Vol. I, II
• Uniform Asymptotic Formula for Orthogonal Polynomials with Exponential Weight