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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=-11/8, b>=a > For fixed z and a=-11/8, b=39/8





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









  


  








Input Form





Hypergeometric2F1[-(11/8), 39/8, 3, z] == (1/(140821065 Pi z^2)) (128 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-8 (1540 + 15015 z - 286416 z^2 + 371280 z^3) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-385 + 216216 z - 541008 z^2 + 297024 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 4 (1540 + 15015 z - 286416 z^2 + 371280 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (1/Sqrt[1 - z]) (3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (385 + 370370 z - 1092624 z^2 + 742560 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])])))








Standard Form





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MathML Form







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