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variants of this functions
Hypergeometric2F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Identities > Recurrence identities > Distant neighbors





http://functions.wolfram.com/07.23.17.0143.01









  


  








Input Form





Hypergeometric2F1[a, b, c, z] == Subscript[\[ScriptCapitalC], n][a, b, c, z] Hypergeometric2F1[a, b + n, c, z] + (((n + b) (z - 1))/(n + b - c)) Subscript[\[ScriptCapitalC], n - 1][a, b, c, z] Hypergeometric2F1[a, b + n + 1, c, z] /; Subscript[\[ScriptCapitalC], 0][a, b, c, z] == 1 && Subscript[\[ScriptCapitalC], 1][a, b, c, z] == (2 + 2 a - b + z)/(1 + a - b) && Subscript[\[ScriptCapitalC], n][a, b, c, z] == ((2 n + 2 b - c + (a - b - n) z)/(n + b - c)) Subscript[\[ScriptCapitalC], n - 1][a, b, c, z] + (((n - 1 + b) (z - 1))/(n - 1 + b - c)) 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