Geodesic
Generalisations of Some Hypergeometric Function Transformations
Glasgow mathematical journal, Tome 1 (1952) no. 1, pp. 38-41

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The formulaewhere γ = 1⁄2 (α + β + l), andwhere γ = 1 + β, were given by Gauss (Ges. Werke, iii, pp. 225, 226). It is here proposed to find the corresponding expressions for the hypergeometric function when γ has general values (not zero or negative integral). These will be derived in section 2 by applying Lagrange's expansionwhereand that root of equation (4) in x is taken which is equal to λ when w = 0. Two generalisations of Whipple's Transformation will be obtained in section 3. 
Macrobert, T. M. Generalisations of Some Hypergeometric Function Transformations. Glasgow mathematical journal, Tome 1 (1952) no. 1, pp. 38-41. doi: 10.1017/S2040618500032925
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