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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=-21/8, b>=a > For fixed z and a=-21/8, b=41/8





http://functions.wolfram.com/07.23.03.bm3k.01









  


  










Input Form





Hypergeometric2F1[-(21/8), 41/8, 3, z] == (256 2^(1/4) (16 Sqrt[1 - z] (-4641 - 69615 z + 5487086 z^2 - 18574248 z^3 + 14536368 z^4) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + 8 Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-4641 - 69615 z + 5487086 z^2 - 18574248 z^3 + 14536368 z^4) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 8 Sqrt[1 - z] (-4641 - 69615 z + 5487086 z^2 - 18574248 z^3 + 14536368 z^4) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (-37128 - 533715 z + 12152248 z^2 - 30534064 z^3 + 19381824 z^4) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (4108329225 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^2)










Standard Form





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MathML Form







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<apply> <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