Asymptotic expansion of Legendre polynomials with respect to the index near \(x = 1\): generalization of the Mehler-Rayleigh formula

DOI10.1134/S0965542520070027zbMath1450.33011OpenAlexW3047769697MaRDI QIDQ2207622

E. A. Tropp, L. A. Bakaleinikov

Publication date: 23 October 2020

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0965542520070027

zbMATH Keywords

Legendre polynomialsuniform asymptotic expansionMehler-Rayleigh formula

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Computation of special functions and constants, construction of tables (65D20)

Related Items (1)

Asymptotic behaviour of level sets of needlet random fields

Cites Work

• Unnamed Item
• Mehler-Heine asymptotics for multiple orthogonal polynomials
• The asymptotic expansion of legendre function of large degree and order

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