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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=-7/4, b>=a > For fixed z and a=-7/4, b=5/4





http://functions.wolfram.com/07.23.03.af0l.01









  


  








Input Form





Hypergeometric2F1[-(7/4), 5/4, 6, -z] == (16384 Sqrt[2] (Sqrt[1 + z] (2048 + 11808 z + 27747 z^2 + 32947 z^3 + 17325 z^4 + 9405 z^5 + 1760 z^6) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] + (2048 + 13856 z + 39555 z^2 + 60694 z^3 + 50272 z^4 + 26730 z^5 + 11165 z^6 + 1760 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (2048 + 13344 z + 36459 z^2 + 52993 z^3 + 40425 z^4 + 2475 z^5 + 440 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (2048 + 11808 z + 27747 z^2 + 32947 z^3 + 17325 z^4 + 9405 z^5 + 1760 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (149906295 Pi z^5 Sqrt[1 + Sqrt[1 + z]])








Standard Form





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MathML Form







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</apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 149906295 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </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='rational'> 1 <sep /> 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