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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=-1/8





http://functions.wolfram.com/07.23.03.bmf3.01









  


  










Input Form





Hypergeometric2F1[-(19/8), -(1/8), 3, z] == (1/(30218265 Pi z^2)) (128 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-8 (836 - 7733 z - 152547 z^2 - 2091 z^3 + 255 z^4) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-209 - 76912 z - 4029 z^2 + 510 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-209 + 49115 z + 17289 z^2 - 1887 z^3 + 204 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 4 (836 - 7733 z - 152547 z^2 - 2091 z^3 + 255 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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</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> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02