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Elliptic Integrals in Terms of Legendre Polynomials

Published online by Cambridge University Press:  18 May 2009

M. O. González
M. O. González
Affiliation:
University of Alabama, U.S.A.
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Consider the elliptic integral of the first kind

or, alternatively,

where x = sin ϕ. It is customary in the theory of elliptic integrals to let k = sin α, k' = cos α, sot that k'2 + k2 = 1. For convenience we shall also introduce the parameter

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 2 , Issue 2 , October 1954 , pp. 97 - 99
Copyright
Copyright © Glasgow Mathematical Journal Trust 1954