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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 4 and fixed z > For fixed z and a=-19/4, b>=a > For fixed z and a=-19/4, b=17/4





http://functions.wolfram.com/07.23.03.a9r3.01









  


  








Input Form





Hypergeometric2F1[-(19/4), 17/4, 2, -z] == (8 Sqrt[2] (Sqrt[1 + z] (65835 + 8941301 z + 67744640 z^2 + 167589888 z^3 + 167444480 z^4 + 58720256 z^5) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] + (65835 + 9007136 z + 76685941 z^2 + 235334528 z^3 + 335034368 z^4 + 226164736 z^5 + 58720256 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (65835 + 4069511 z + 24465392 z^2 + 51778560 z^3 + 45989888 z^4 + 14680064 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (65835 + 8941301 z + 67744640 z^2 + 167589888 z^3 + 167444480 z^4 + 58720256 z^5) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])]))/(19684665 Pi z Sqrt[1 + Sqrt[1 + z]])








Standard Form





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MathML Form







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type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8941301 </cn> <ci> z </ci> </apply> <cn type='integer'> 65835 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </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