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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=-23/4, b>=a > For fixed z and a=-23/4, b=-3/4





http://functions.wolfram.com/07.23.03.9375.01









  


  








Input Form





Hypergeometric2F1[-(23/4), -(3/4), 1, -z] == (1/(504735 Pi Sqrt[1 + Sqrt[1 + z]])) (2 Sqrt[2] ((-Sqrt[1 + z]) (-536639 + 660267 z + 359811 z^2 + 165049 z^3 + 47328 z^4 + 6144 z^5) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-536639 + 123628 z + 1020078 z^2 + 524860 z^3 + 212377 z^4 + 53472 z^5 + 6144 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + 8 (-3988 - 235917 z + 12519 z^2 + 5549 z^3 + 1533 z^4 + 192 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + Sqrt[1 + z] (-536639 + 660267 z + 359811 z^2 + 165049 z^3 + 47328 z^4 + 6144 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))








Standard Form





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MathML Form







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<apply> <times /> <cn type='integer'> 359811 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 660267 </cn> <ci> z </ci> </apply> <cn type='integer'> -536639 </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> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02