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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=-11/4, b>=a > For fixed z and a=-11/4, b=-3/4





http://functions.wolfram.com/07.23.03.ad3p.01









  


  








Input Form





Hypergeometric2F1[-(11/4), -(3/4), 6, -z] == (16384 Sqrt[2] ((-Sqrt[1 + z]) (2048 + 21664 z + 109971 z^2 + 378664 z^3 + 1229306 z^4 - 3129588 z^5 + 181355 z^6 + 8740 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (2048 + 23712 z + 131635 z^2 + 488635 z^3 + 1607970 z^4 - 1900282 z^5 - 2948233 z^6 + 190095 z^7 + 8740 z^8) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (2048 + 23200 z + 126075 z^2 + 459685 z^3 + 1506230 z^4 + 5280978 z^5 - 4354705 z^6 + 2185 z^7) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] + Sqrt[1 + z] (2048 + 21664 z + 109971 z^2 + 378664 z^3 + 1229306 z^4 - 3129588 z^5 + 181355 z^6 + 8740 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (61538805405 Pi z^5 Sqrt[1 + Sqrt[1 + z]])








Standard Form





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MathML Form







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<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> <power /> <apply> <times /> <cn type='integer'> 61538805405 </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