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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=-21/8, b>=a > For fixed z and a=-21/8, b=39/8





http://functions.wolfram.com/07.23.03.bm1q.01









  


  










Input Form





Hypergeometric2F1[-(21/8), 39/8, 1, z] == -((2 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-197829 + 1608928 z - 3162368 z^2 + 1757184 z^3) EllipticE[ 1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (-126586 + 197829 Sqrt[1 - z] + 197829 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] - 16 (-181203 + 100558 Sqrt[1 - z] + 100558 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z + 128 (-91793 + 24706 Sqrt[1 - z] + 24706 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^2 - 67584 (-237 + 26 Sqrt[1 - z] + 26 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^3 - 7028736 z^4) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (324415 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(5/4)))










Standard Form





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MathML Form







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</apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 324415 </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> </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'> 5 <sep /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02