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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 4 and fixed z > For fixed z and a=1/4, b>=a > For fixed z and a=1/4, b=1/4





http://functions.wolfram.com/07.23.03.ahz2.01









  


  










Input Form





Hypergeometric2F1[1/4, 1/4, 11/2, z] == (1/(732615 Pi^(3/2) z^(9/2))) (224 (-2 (1680 - 8460 z + 17341 z^2 - 18806 z^3 + 14389 z^4) EllipticE[(1/2) (1 - Sqrt[z])] + 2 (1680 - 8460 z + 17341 z^2 - 18806 z^3 + 14389 z^4) EllipticE[(1/2) (1 + Sqrt[z])] + (1680 + 840 Sqrt[z] - 8460 z - 4160 z^(3/2) + 17341 z^2 + 8353 z^(5/2) - 18806 z^3 - 8834 z^(7/2) + 14389 z^4 + 9945 z^(9/2)) EllipticK[(1/2) (1 - Sqrt[z])] + (-1680 + 840 Sqrt[z] + 8460 z - 4160 z^(3/2) - 17341 z^2 + 8353 z^(5/2) + 18806 z^3 - 8834 z^(7/2) - 14389 z^4 + 9945 z^(9/2)) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)










Standard Form





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MathML Form







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<apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <cn type='integer'> 2 </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