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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=-15/4, b>=a > For fixed z and a=-15/4, b=21/4





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









  


  








Input Form





Hypergeometric2F1[-(15/4), 21/4, 3, -z] == (64 Sqrt[2] (Sqrt[1 + z] (-13860 + 266805 z + 17684864 z^2 + 83933184 z^3 + 125239296 z^4 + 58720256 z^5) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] + (-13860 + 252945 z + 17951669 z^2 + 101618048 z^3 + 209172480 z^4 + 183959552 z^5 + 58720256 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 2 (-6930 + 128205 z + 3714232 z^2 + 13948416 z^3 + 17719296 z^4 + 7340032 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-13860 + 266805 z + 17684864 z^2 + 83933184 z^3 + 125239296 z^4 + 58720256 z^5) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])]))/(334639305 Pi z^2 Sqrt[1 + Sqrt[1 + z]])








Standard Form





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MathML Form







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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'> 334639305 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </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