Geodesic
Elliptic Integrals in Terms of Legendre Polynomials
Glasgow mathematical journal, Tome 2 (1954) no. 2, pp. 97-99

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Consider the elliptic integral of the first kindor, 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 
González, M. O. Elliptic Integrals in Terms of Legendre Polynomials. Glasgow mathematical journal, Tome 2 (1954) no. 2, pp. 97-99. doi: 10.1017/S2040618500033104
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     title = {Elliptic {Integrals} in {Terms} of {Legendre} {Polynomials}},
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