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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=-47/8, b>=a > For fixed z and a=-47/8, b=-13/8





http://functions.wolfram.com/07.23.03.b4vv.01









  


  










Input Form





Hypergeometric2F1[-(47/8), -(13/8), 4, z] == (2048 2^(1/4) (-2 Sqrt[1 - z] (-55762304 + 1113939151 z - 15732375659 z^2 - 307150687858 z^3 - 365280049918 z^4 - 19492569733 z^5 + 2774916417 z^6 - 335780328 z^7 + 21760440 z^8) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-55762304 + 1113939151 z - 15732375659 z^2 - 307150687858 z^3 - 365280049918 z^4 - 19492569733 z^5 + 2774916417 z^6 - 335780328 z^7 + 21760440 z^8) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[1 - z] (-55762304 + 1113939151 z - 15732375659 z^2 - 307150687858 z^3 - 365280049918 z^4 - 19492569733 z^5 + 2774916417 z^6 - 335780328 z^7 + 21760440 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (-55762304 + 1148790591 z - 16422869814 z^2 + 488692835617 z^3 + 1667653824312 z^4 + 712225520097 z^5 - 41957782958 z^6 + 5913859887 z^7 - 695497140 z^8 + 43520880 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (804989266676595 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^3)










Standard Form





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MathML Form







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<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> <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 /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 21760440 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn 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Rule Form





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





2007-05-02