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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/07.23.17.0145.01









  


  








Input Form





Hypergeometric2F1[a, b, c, z] == Subscript[\[ScriptCapitalC], n][a, b, c, z] Hypergeometric2F1[a, b, c + n, z] - (((a - n - c) (b - n - c) z)/((n + c - 1) (n + c) (z - 1))) Subscript[\[ScriptCapitalC], n - 1][a, b, c, z] Hypergeometric2F1[a, b, c + n + 1, z] /; Subscript[\[ScriptCapitalC], 0][a, b, c, z] == 1 && Subscript[\[ScriptCapitalC], 1][a, b, c, z] == (-c + (1 - a - b + 2 c) z)/ (c (z - 1)) && Subscript[\[ScriptCapitalC], n][a, b, c, z] == ((1 - n - c + (1 - a - b + 2 (n - 1 + c)) z)/((n - 1 + c) (z - 1))) Subscript[\[ScriptCapitalC], n - 1][a, b, c, z] - (((a - c - n + 1) (b - c - n + 1) z)/((n - 2 + c) (n - 1 + c) (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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</ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -2 </cn> </apply> </apply> <ci> a </ci> <ci> b </ci> <ci> c </ci> <ci> z </ci> </apply> </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