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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=-17/4, b>=a > For fixed z and a=-17/4, b=3/4





http://functions.wolfram.com/07.23.03.aaj7.01









  


  








Input Form





Hypergeometric2F1[-(17/4), 3/4, 3, -z] == (64 Sqrt[2] ((-2652 - 20553 z + 59525 z^2 + 59525 z^3 + 37875 z^4 + 13472 z^5 + 2048 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + Sqrt[1 + z] (-2652 - 20553 z + 59525 z^2 + 59525 z^3 + 37875 z^4 + 13472 z^5 + 2048 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 2 Sqrt[1 + z] (-1326 - 9945 z + 4900 z^2 + 3675 z^3 + 1500 z^4 + 256 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-2652 - 20553 z + 59525 z^2 + 59525 z^3 + 37875 z^4 + 13472 z^5 + 2048 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (1740375 Pi z^2 Sqrt[1 + Sqrt[1 + z]])








Standard Form





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MathML Form







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2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </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