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variants of this functions
Hypergeometric2F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > For rational parameters with denominators 3 and fixed z > For fixed z and a=1/3, b>=a > For fixed z and a=1/3, b=17/3





http://functions.wolfram.com/07.23.03.7592.01









  


  








Input Form





Hypergeometric2F1[1/3, 17/3, -(5/2), -z] == (1/(414720 (1 + z)^(17/2))) ((414720 + 3861504 z + 17016832 z^2 + 58462208 z^3 + 17785179 z^4 + 11150436 z^5 + 4804472 z^6 + 1232160 z^7 + 141440 z^8) Cosh[ArcSinh[Sqrt[z]]/3] + Sqrt[z] Sqrt[1 + z] (-138240 - 1189888 z - 4845568 z^2 + 13665263 z^3 + 9166060 z^4 + 4241432 z^5 + 1161440 z^6 + 141440 z^7) Sinh[ArcSinh[Sqrt[z]]/3])








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