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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 4 and fixed z > For fixed z and a=-15/4, b>=a > For fixed z and a=-15/4, b=13/4





http://functions.wolfram.com/07.23.03.abm2.01









  


  








Input Form





Hypergeometric2F1[-(15/4), 13/4, 2, -z] == (1/(65835 Pi z Sqrt[1 + Sqrt[1 + z]])) (8 Sqrt[2] (Sqrt[1 + z] (385 + 27679 z + 119424 z^2 + 157696 z^3 + 65536 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (385 + 28064 z + 147103 z^2 + 277120 z^3 + 223232 z^4 + 65536 z^5) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (385 + 11509 z + 38832 z^2 + 44032 z^3 + 16384 z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (385 + 27679 z + 119424 z^2 + 157696 z^3 + 65536 z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))








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