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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=-19/4, b>=a > For fixed z and a=-19/4, b=-3/4





http://functions.wolfram.com/07.23.03.a9ad.01









  


  








Input Form





Hypergeometric2F1[-(19/4), -(3/4), 4, -z] == (256 Sqrt[2] ((-Sqrt[1 + z]) (608 + 8493 z + 77292 z^2 - 660170 z^3 + 142284 z^4 + 27333 z^5 + 4496 z^6 + 384 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (608 + 9101 z + 85785 z^2 - 582878 z^3 - 517886 z^4 + 169617 z^5 + 31829 z^6 + 4880 z^7 + 384 z^8) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] + (608 + 8949 z + 83619 z^2 + 497386 z^3 - 1269090 z^4 + 7137 z^5 + 1151 z^6 + 96 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + Sqrt[1 + z] (608 + 8493 z + 77292 z^2 - 660170 z^3 + 142284 z^4 + 27333 z^5 + 4496 z^6 + 384 z^7) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])]))/(140821065 Pi z^3 Sqrt[1 + Sqrt[1 + z]])








Standard Form





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MathML Form







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</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'> 140821065 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </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