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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=5/4





http://functions.wolfram.com/07.23.03.abf4.01









  


  








Input Form





Hypergeometric2F1[-(15/4), 5/4, 5, -z] == (4096 Sqrt[2] (Sqrt[1 + z] (1920 + 12560 z + 33435 z^2 + 40425 z^3 + 56977 z^4 + 38547 z^5 + 13728 z^6 + 2048 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (1920 + 14480 z + 45995 z^2 + 73860 z^3 + 97402 z^4 + 95524 z^5 + 52275 z^6 + 15776 z^7 + 2048 z^8) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - 8 (240 + 1750 z + 5340 z^2 + 8085 z^3 + 2069 z^4 + 1317 z^5 + 447 z^6 + 64 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (1920 + 12560 z + 33435 z^2 + 40425 z^3 + 56977 z^4 + 38547 z^5 + 13728 z^6 + 2048 z^7) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])]))/(140821065 Pi z^4 Sqrt[1 + Sqrt[1 + z]])








Standard Form





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MathML Form







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</apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 140821065 </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> </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