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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=1/4





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









  


  








Input Form





Hypergeometric2F1[-(7/4), 1/4, 5, -z] == (4096 Sqrt[2] (2 Sqrt[1 + z] (-64 - 424 z - 1271 z^2 - 2616 z^3 + 1045 z^4 + 110 z^5) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + 2 (-64 - 488 z - 1695 z^2 - 3887 z^3 - 1571 z^4 + 1155 z^5 + 110 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-128 - 944 z - 3169 z^2 - 7083 z^3 - 15235 z^4 + 55 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 2 Sqrt[1 + z] (-64 - 424 z - 1271 z^2 - 2616 z^3 + 1045 z^4 + 110 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (27760425 Pi z^4 Sqrt[1 + Sqrt[1 + z]])








Standard Form





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MathML Form







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<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