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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 8 and fixed z and a<0 > For fixed z and a=-39/8, b>=a > For fixed z and a=-39/8, b=-13/8





http://functions.wolfram.com/07.23.03.b9vq.01









  


  










Input Form





Hypergeometric2F1[-(39/8), -(13/8), 5, z] == (65536 2^(1/4) (2 Sqrt[1 - z] (-9491456 + 152753120 z - 1355730285 z^2 + 11223136925 z^3 + 126634774210 z^4 + 95483126970 z^5 + 2804795175 z^6 - 233715495 z^7 + 12554100 z^8) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-9491456 + 152753120 z - 1355730285 z^2 + 11223136925 z^3 + 126634774210 z^4 + 95483126970 z^5 + 2804795175 z^6 - 233715495 z^7 + 12554100 z^8) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (-9491456 + 152753120 z - 1355730285 z^2 + 11223136925 z^3 + 126634774210 z^4 + 95483126970 z^5 + 2804795175 z^6 - 233715495 z^7 + 12554100 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 4 (-2372864 + 39671320 z - 362556935 z^2 + 3013815350 z^3 - 62185644535 z^4 - 137828587330 z^5 - 38738395605 z^6 + 1465900410 z^7 - 120310125 z^8 + 6277050 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (12074839000148925 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^4)










Standard Form





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MathML Form







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type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 12074839000148925 </cn> <pi /> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <cn type='integer'> 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Rule Form





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





2007-05-02