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variants of this functions
Hypergeometric2F1Regularized




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1Regularized[a,b,c,z] > Identities > Functional identities > Quadratic transformations with fixed a,b,z





http://functions.wolfram.com/07.24.17.0104.01









  


  








Input Form





Hypergeometric2F1Regularized[a, b, 1/2, z] == (((Gamma[a + 1/2] Gamma[1 - b])/(2 Pi)) (Hypergeometric2F1Regularized[2 a, 1 - 2 b, a - b + 1, (Sqrt[1 - z] + Sqrt[-z])/(2 Sqrt[1 - z])] + Hypergeometric2F1Regularized[2 a, 1 - 2 b, a - b + 1, (Sqrt[1 - z] - Sqrt[-z])/(2 Sqrt[1 - z])]))/(1 - z)^a /; !IntervalMemberQ[Interval[{1, Infinity}], z]








Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29