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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=-41/8, b>=a > For fixed z and a=-41/8, b=-37/8





http://functions.wolfram.com/07.23.03.b8o5.01









  


  










Input Form





Hypergeometric2F1[-(41/8), -(37/8), 3, z] == (256 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-4277879320 + 201595062955 z + 40733543989626 z^2 + 274885998670721 z^3 + 452068534696996 z^4 + 216002443915965 z^5 + 26041050970970 z^6 + 360935884855 z^7) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + 4 (1069469830 - 50799816925 z - 3207501663774 z^2 - 12212123755145 z^3 - 2214961576510 z^4 + 12355742574609 z^5 + 5021306144470 z^6 + 307268623445 z^7) EllipticK[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - Sqrt[1 - z] (-4277879320 + 201595062955 z + 40733543989626 z^2 + 274885998670721 z^3 + 452068534696996 z^4 + 216002443915965 z^5 + 26041050970970 z^6 + 360935884855 z^7) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-4277879320 + 201595062955 z + 40733543989626 z^2 + 274885998670721 z^3 + 452068534696996 z^4 + 216002443915965 z^5 + 26041050970970 z^6 + 360935884855 z^7) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (3562032362964075 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(1/4) z^2)










Standard Form





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MathML Form







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<apply> <times /> <cn type='integer'> -1 </cn> <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> <plus /> <apply> <times /> <cn type='integer'> 360935884855 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 26041050970970 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 216002443915965 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 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Rule Form





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





2007-05-02