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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=-17/4, b>=a > For fixed z and a=-17/4, b=7/4





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









  


  










Input Form





Hypergeometric2F1[-(17/4), 7/4, 5, -z] == (4096 Sqrt[2] (4 (7072 + 43316 z + 96577 z^2 + 46410 z^3 + 254700 z^4 + 318858 z^5 + 207259 z^6 + 71168 z^7 + 10240 z^8) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + 4 Sqrt[1 + z] (7072 + 43316 z + 96577 z^2 + 46410 z^3 + 254700 z^4 + 318858 z^5 + 207259 z^6 + 71168 z^7 + 10240 z^8) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (28288 + 166192 z + 348075 z^2 + 116025 z^3 + 206625 z^4 + 162147 z^5 + 63808 z^6 + 10240 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 4 (7072 + 43316 z + 96577 z^2 + 46410 z^3 + 254700 z^4 + 318858 z^5 + 207259 z^6 + 71168 z^7 + 10240 z^8) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (1665538875 Pi z^4 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'> 43316 </cn> <ci> z </ci> </apply> <cn type='integer'> 7072 </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> <power /> <apply> <times /> <cn type='integer'> 1665538875 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </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> 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Rule Form





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





2007-05-02