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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=-35/8, b>=a > For fixed z and a=-35/8, b=31/8





http://functions.wolfram.com/07.23.03.bd3i.01









  


  










Input Form





Hypergeometric2F1[-(35/8), 31/8, 2, z] == (1/(39066489 Pi z)) (8 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (-39501 + 3272333 z - 20240336 z^2 + 43238208 z^3 - 38528256 z^4 + 12305280 z^5) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 12 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (408177 - 3366442 z + 8591596 z^2 - 8709168 z^3 + 3076320 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 2 (-39501 + 3272333 z - 20240336 z^2 + 43238208 z^3 - 38528256 z^4 + 12305280 z^5) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-4858623 + 42023095 z - 123256120 z^2 + 164370960 z^3 - 102897600 z^4 + 24610560 z^5) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))










Standard Form





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MathML Form







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</apply> <apply> <times /> <cn type='integer'> 42023095 </cn> <ci> z </ci> </apply> <cn type='integer'> -4858623 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <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> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02