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Legendre functions

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Functions that are solutions of the Legendre equation

(*)

where and are arbitrary numbers. If and , then the solutions of equation (*), restricted to , are called Legendre polynomials; for integers with , the solutions of equation (*), restricted to , are called Legendre associated functions.


Comments

References

[a1] M. Abramowitz, I.A. Stegun, "Handbook of mathematical functions" , Dover, reprint (1965) pp. Chapt. 8
[a2] N.N. Lebedev, "Special functions and their applications" , Dover, reprint (1972) (Translated from Russian)
How to Cite This Entry:
Legendre functions. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Legendre_functions&oldid=15230
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article