Note on the Integrals of Products of Associated Legendre Functions | Zendy

J. A. Grant | Zendy; O. G. Ludwigt | Zendy

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Note on the Integrals of Products of Associated Legendre Functions

Author(s) -

J. A. Grant,

O. G. Ludwigt

Publication year - 1964

Publication title -

the computer journal

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.319

H-Index - 64

eISSN - 1460-2067

pISSN - 0010-4620

DOI - 10.1093/comjnl/6.4.356

Subject(s) - quadrature (astronomy) , mathematics , legendre polynomials , polynomial , legendre function , gaussian quadrature , gaussian , function (biology) , expression (computer science) , pure mathematics , mathematical analysis , computer science , computational chemistry , physics , integral equation , chemistry , nyström method , evolutionary biology , optics , biology , programming language

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.

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