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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=15/4





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









  


  










Input Form





Hypergeometric2F1[-(17/4), 15/4, 4, -z] == (256 Sqrt[2] ((21216 - 59007 z + 319566 z^2 + 9424765 z^3 + 30253760 z^4 + 39637504 z^5 + 23887872 z^6 + 5505024 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + Sqrt[1 + z] (21216 - 59007 z + 319566 z^2 + 9424765 z^3 + 30253760 z^4 + 39637504 z^5 + 23887872 z^6 + 5505024 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (21216 - 64311 z + 338130 z^2 + 3258865 z^3 + 6428800 z^4 + 4982784 z^5 + 1376256 z^6) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - (21216 - 59007 z + 319566 z^2 + 9424765 z^3 + 30253760 z^4 + 39637504 z^5 + 23887872 z^6 + 5505024 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (777251475 Pi z^3 Sqrt[1 + Sqrt[1 + z]])










Standard Form





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MathML Form







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3 </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='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02