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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=-17/8, b>=a > For fixed z and a=-17/8, b=45/8





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









  


  










Input Form





Hypergeometric2F1[-(17/8), 45/8, 3, z] == (1/(4108329225 Pi z^2)) (128 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (32 (-4641 - 69615 z + 5487086 z^2 - 18574248 z^3 + 14536368 z^4) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-4641 + 6348888 z - 23611984 z^2 + 19381824 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 16 (-4641 - 69615 z + 5487086 z^2 - 18574248 z^3 + 14536368 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (1/Sqrt[1 - z]) (3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-4641 - 10767120 z + 53985536 z^2 - 81834368 z^3 + 38763648 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])])))










Standard Form





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MathML Form







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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 /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </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