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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=15/8, b>=a > For fixed z and a=15/8, b=35/8





http://functions.wolfram.com/07.23.03.c5g8.01









  


  








Input Form





Hypergeometric2F1[15/8, 35/8, 1, z] == (2 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (25943 + 32046 z - 5733 z^2 + 784 z^3) EllipticE[ 1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - (-13558 + 25943 Sqrt[1 - z] + 25943 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] + 6 (-15208 + 5341 Sqrt[1 - z] + 5341 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z - 147 (10 + 39 Sqrt[1 - z] + 39 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^2 + 196 (1 + 4 Sqrt[1 - z] + 4 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^3) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/(39501 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(21/4))








Standard Form





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MathML Form







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type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 21 <sep /> 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