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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=-19/8





http://functions.wolfram.com/07.23.03.b9tu.01









  


  










Input Form





Hypergeometric2F1[-(39/8), -(19/8), 4, z] == (2048 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-22542208 + 469688037 z - 7023130569 z^2 - 214178071730 z^3 - 398704972050 z^4 - 126781233327 z^5 - 462569877 z^6 + 18441324 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-22542208 + 469688037 z - 7023130569 z^2 - 214178071730 z^3 - 398704972050 z^4 - 126781233327 z^5 - 462569877 z^6 + 18441324 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[1 - z] (-22542208 + 469688037 z - 7023130569 z^2 - 214178071730 z^3 - 398704972050 z^4 - 126781233327 z^5 - 462569877 z^6 + 18441324 z^7) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (-22542208 + 478141365 z - 7196952126 z^2 + 167781855619 z^3 + 750776182380 z^4 + 533126715723 z^5 + 50237240130 z^6 - 1885625379 z^7 + 73765296 z^8) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (388478143278225 Pi (1 + Sqrt[1 - z])^(1/4) z^3)










Standard Form





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MathML Form







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<sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <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 /> 4 </cn> </apply> <apply> <power /> <apply> <times /> <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> <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> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 73765296 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1885625379 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 50237240130 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 533126715723 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 750776182380 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 167781855619 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 7196952126 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 478141365 </cn> <ci> z </ci> </apply> <cn type='integer'> -22542208 </cn> 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Rule Form





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





2007-05-02