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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=3/8, b>=a > For fixed z and a=3/8, b=41/8





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









  


  








Input Form





Hypergeometric2F1[3/8, 41/8, 5, z] == (65536 2^(1/4) ((2 (-1024 - 928 z - 1177 z^2 - 2156 z^3 + 18480 z^4) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])])/ Sqrt[1 - z] + (1/Sqrt[1 - z]) (Sqrt[2 - 2 Sqrt[1 - z]] (-1024 - 928 z - 1177 z^2 - 2156 z^3 + 18480 z^4) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]) + 4 (256 + 328 z + 451 z^2 + 770 z^3) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - ((-1024 - 928 z - 1177 z^2 - 2156 z^3 + 18480 z^4) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])])/ Sqrt[1 - z]))/(555179625 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^4)








Standard Form





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MathML Form







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<apply> <power /> <apply> <times /> <cn type='integer'> 555179625 </cn> <pi /> <apply> <power /> <apply> <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='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </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