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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/07.24.17.0142.01









  


  








Input Form





Hypergeometric2F1Regularized[a, b, c, z] == ((1 - z)/((n + a - c) (n + b - c) z)) Subscript[\[ScriptCapitalC], n - 1][ a, b, c, z] Hypergeometric2F1Regularized[a, b, c - n - 1, z] + Subscript[\[ScriptCapitalC], n][a, b, c, z] Hypergeometric2F1Regularized[ a, b, c - n, z] /; Subscript[\[ScriptCapitalC], 0][a, b, c, z] == 1 && Subscript[\[ScriptCapitalC], 1][a, b, c, z] == (2 - c - (3 + a + b - 2 c) z)/((1 + a - c) (1 + b - c) z) && Subscript[\[ScriptCapitalC], n][a, b, c, z] == ((n + 1 - c - (1 + a + b + 2 (n - c)) z)/((n + a - c) (n + b - c) z)) Subscript[\[ScriptCapitalC], n - 1][a, b, c, z] + ((1 - z)/((n - 1 + a - c) (n - 1 + b - c) z)) 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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</ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <ci> a </ci> <ci> b </ci> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02