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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=-13/8, b>=a > For fixed z and a=-13/8, b=39/8





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









  


  








Input Form





Hypergeometric2F1[-(13/8), 39/8, 2, z] == (16 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-1495 + 54564 z - 153600 z^2 + 101376 z^3) EllipticE[ 1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (1495 (1 + Sqrt[1 - z] + Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) + (66531 - 54564 Sqrt[1 - z] - 54564 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z + 96 (-4891 + 1600 Sqrt[1 - z] + 1600 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^2 - 2304 (-351 + 44 Sqrt[1 - z] + 44 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^3 - 405504 z^4) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (973245 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(5/4) z)








Standard Form





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MathML Form







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type='integer'> 973245 </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> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02