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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=-5/4, b>=a > For fixed z and a=-5/4, b=23/4





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









  


  








Input Form





Hypergeometric2F1[-(5/4), 23/4, 6, -z] == (16384 Sqrt[2] ((2048 - 2528 z + 3875 z^2 - 7475 z^3 + 22400 z^4 + 243712 z^5 + 196608 z^6) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] + Sqrt[1 + z] (2048 - 2528 z + 3875 z^2 - 7475 z^3 + 22400 z^4 + 243712 z^5 + 196608 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (2048 - 3040 z + 4875 z^2 - 9200 z^3 + 25600 z^4 + 49152 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (2048 - 2528 z + 3875 z^2 - 7475 z^3 + 22400 z^4 + 243712 z^5 + 196608 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (1527701175 Pi z^5 Sqrt[1 + Sqrt[1 + z]])








Standard Form





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MathML Form







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</apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 1527701175 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </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