Asymptotic Expansion of Legendre Polynomials with Respect to the Index near x = 1: Generalization of the Mehler–Rayleigh Formula

An asymptotic expansion of the Legendre polynomials in inverse powers of the index in a neighborhood of is obtained. It is shown that the expansion coefficient of is a linear combination of terms of the form , where . It is also shown that the first terms of the expansion coincide with a well-known...

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Veröffentlicht in:	Computational mathematics and mathematical physics 2020-07, Vol.60 (7), p.1155-1162
Hauptverfasser:	Bakaleinikov, L. A., Tropp, E. A.
Format:	Artikel
Sprache:	eng
Schlagworte:	Asymptotic series Computational Mathematics and Numerical Analysis Mathematics Mathematics and Statistics Polynomials Thermal expansion
Online-Zugang:	Volltext
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