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Note on the Integrals of Products of Associated Legendre Functions

Note on the integrals of products of associated Legendre functions
descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1964 English Publisher:Oxford University Press (OUP)Journal:The Computer Journal, volume 6, pages 356-357 (issn: 0010-4620, eissn: 1460-2067, Copyright policy )
Authors: J. A. Grant; Oliver G. Ludwig;

doi: 10.1093/comjnl/6.4.356

Note on the Integrals of Products of Associated Legendre Functions

Abstract

Although closed-form expressions are available in particular cases (Gaunt, 1929), they are, in general, unattractive for machine use. Other expressions for the general case have been given (Miller, 1963; Joy, 1962), but have been found comparatively less convenient for the computation of IK than the method suggested in the present work. This method, which is based on Gaussian quadrature techniques, is theoretically exact and also reasonably stable computationally.

Keywords

special functions

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
5
Average
Top 10%
Average
bronze