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Generalisations of Some Hypergeometric Function Transformations
Published online by Cambridge University Press: 18 May 2009
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The formulae
where γ = ½ (α + β + l), and
where 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 expansion
where
and 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.
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- Research Article
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- Copyright © Glasgow Mathematical Journal Trust 1952
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