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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=-3/4, b>=a > For fixed z and a=-3/4, b=5/4





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









  


  








Input Form





Hypergeometric2F1[-(3/4), 5/4, 6, -z] == (16384 Sqrt[2] (Sqrt[1 + z] (2048 + 9888 z + 18707 z^2 + 16782 z^3 + 5775 z^4 + 1540 z^5) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (2048 + 11936 z + 28595 z^2 + 35489 z^3 + 22557 z^4 + 7315 z^5 + 1540 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (2048 + 11424 z + 25979 z^2 + 30183 z^3 + 17325 z^4 + 385 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (2048 + 9888 z + 18707 z^2 + 16782 z^3 + 5775 z^4 + 1540 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (38864595 Pi z^5 Sqrt[1 + Sqrt[1 + z]])








Standard Form





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MathML Form







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<cn type='integer'> 9888 </cn> <ci> z </ci> </apply> <cn type='integer'> 2048 </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> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02