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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=-19/4, b>=a > For fixed z and a=-19/4, b=-3/4





http://functions.wolfram.com/07.23.03.a9a9.01









  


  








Input Form





Hypergeometric2F1[-(19/4), -(3/4), 3, -z] == (64 Sqrt[2] (-4 Sqrt[1 + z] (95 + 1710 z - 23832 z^2 + 7126 z^3 + 1665 z^4 + 324 z^5 + 32 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 4 (95 + 1805 z - 22122 z^2 - 16706 z^3 + 8791 z^4 + 1989 z^5 + 356 z^6 + 32 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + 4 Sqrt[1 + z] (95 + 1710 z - 23832 z^2 + 7126 z^3 + 1665 z^4 + 324 z^5 + 32 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (380 + 7125 z + 51732 z^2 - 203162 z^3 + 1752 z^4 + 333 z^5 + 32 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (4542615 Pi z^2 Sqrt[1 + Sqrt[1 + z]])








Standard Form





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MathML Form







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</apply> </apply> </apply> </apply> </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