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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=-7/4





http://functions.wolfram.com/07.23.03.9293.01









  


  










Input Form





Hypergeometric2F1[-(23/4), -(7/4), 3, -z] == (64 Sqrt[2] (2 Sqrt[1 + z] (-6118 - 174363 z + 5583240 z^2 - 9435914 z^3 + 1068270 z^4 + 149373 z^5 + 19208 z^6 + 1344 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + 2 (-6118 - 180481 z + 5408877 z^2 - 3852674 z^3 - 8367644 z^4 + 1217643 z^5 + 168581 z^6 + 20552 z^7 + 1344 z^8) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-12236 - 357903 z - 2296179 z^2 + 32983658 z^3 - 29494290 z^4 + 77301 z^5 + 9793 z^6 + 672 z^7) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - 2 Sqrt[1 + z] (-6118 - 174363 z + 5583240 z^2 - 9435914 z^3 + 1068270 z^4 + 149373 z^5 + 19208 z^6 + 1344 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (422463195 Pi z^2 Sqrt[1 + Sqrt[1 + z]])










Standard Form





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MathML Form







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</ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5583240 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 174363 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -6118 </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'> 422463195 </cn> <pi /> <apply> <power /> <ci> z 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Rule Form





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





2007-05-02