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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=-17/8, b>=a > For fixed z and a=-17/8, b=-5/8





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









  


  










Input Form





Hypergeometric2F1[-(17/8), -(5/8), 6, z] == (524288 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-557056 + 5537920 z - 25935795 z^2 + 79723200 z^3 - 215331690 z^4 - 1961176980 z^5 - 295370075 z^6 + 9764300 z^7) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (-557056 + 5746816 z - 27955395 z^2 + 88911615 z^3 - 242850270 z^4 - 92721090 z^5 + 266984305 z^6 + 2441075 z^7) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[1 - z] (-557056 + 5537920 z - 25935795 z^2 + 79723200 z^3 - 215331690 z^4 - 1961176980 z^5 - 295370075 z^6 + 9764300 z^7) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-557056 + 5537920 z - 25935795 z^2 + 79723200 z^3 - 215331690 z^4 - 1961176980 z^5 - 295370075 z^6 + 9764300 z^7) EllipticK[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (470457104542425 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(1/4) z^5)










Standard Form





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MathML Form







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<power /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <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> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 470457104542425 </cn> <pi /> <apply> <power /> <apply> <plus /> <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> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 4 </cn> 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Rule Form





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





2007-05-02