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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=-9/4, b>=a > For fixed z and a=-9/4, b=19/4





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









  


  








Input Form





Hypergeometric2F1[-(9/4), 19/4, 5, -z] == (4096 Sqrt[2] ((-384 + 624 z - 1425 z^2 + 5475 z^3 + 92800 z^4 + 149504 z^5 + 65536 z^6) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] + Sqrt[1 + z] (-384 + 624 z - 1425 z^2 + 5475 z^3 + 92800 z^4 + 149504 z^5 + 65536 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 2 Sqrt[1 + z] (-192 + 360 z - 825 z^2 + 3000 z^3 + 12800 z^4 + 8192 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-384 + 624 z - 1425 z^2 + 5475 z^3 + 92800 z^4 + 149504 z^5 + 65536 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (134008875 Pi z^4 Sqrt[1 + Sqrt[1 + z]])








Standard Form





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MathML Form







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<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