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variants of this functions
Hypergeometric2F1Regularized




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1Regularized[a,b,c,z] > Identities > Recurrence identities > Distant neighbors





http://functions.wolfram.com/07.24.17.0140.01









  


  








Input Form





Hypergeometric2F1Regularized[a, b, c, z] == Subscript[\[ScriptCapitalC], n][a, b, c, z] Hypergeometric2F1Regularized[a, b - n, c, z] + ((n - b + c)/((n - b) (z - 1))) Subscript[\[ScriptCapitalC], n - 1][a, b, c, z] Hypergeometric2F1Regularized[a, b - n - 1, c, z] /; Subscript[\[ScriptCapitalC], 0][a, b, c, z] == 1 && Subscript[\[ScriptCapitalC], 1][a, b, c, z] == (2 - 2 b + c + (b - a - 1) z)/((b - 1) (z - 1)) && Subscript[\[ScriptCapitalC], n][a, b, c, z] == (-((2 n - 2 b + c + (b - a - n) z)/((n - b) (z - 1)))) Subscript[\[ScriptCapitalC], n - 1][a, b, c, z] + ((n - 1 - b + c)/((n - 1 - b) (z - 1))) Subscript[\[ScriptCapitalC], n - 2][a, b, c, z] && Element[n, Integers] && n > 0








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)





2007-05-02