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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=19/8, b>=a > For fixed z and a=19/8, b=39/8





http://functions.wolfram.com/07.23.03.c7ie.01









  


  










Input Form





Hypergeometric2F1[19/8, 39/8, 3, z] == (256 2^(1/4) (-8 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (70 - 350 z - 143 z^2 + 33 z^3) EllipticE[ 1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + 4 Sqrt[1 - z] (70 - 350 z - 143 z^2 + 33 z^3) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + 4 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (70 - 350 z - 143 z^2 + 33 z^3) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (280 - 1505 z + 6358 z^2 - 2541 z^3 + 528 z^4) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (823515 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(17/4) z^2)










Standard Form





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MathML Form







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<power /> <ci> z </ci> <cn type='integer'> 2 </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