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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=1/4





http://functions.wolfram.com/07.23.03.a9d1.01









  


  










Input Form





Hypergeometric2F1[-(19/4), 1/4, 9/2, z] == (1/(618628725 Pi^(3/2) z^(7/2))) (16 (-2 (-175560 + 1860936 z - 10014235 z^2 + 52158876 z^3 + 21737430 z^4 - 9566700 z^5 + 3407157 z^6 - 767520 z^7 + 79872 z^8) EllipticE[(1/2) (1 - Sqrt[z])] + 2 (-175560 + 1860936 z - 10014235 z^2 + 52158876 z^3 + 21737430 z^4 - 9566700 z^5 + 3407157 z^6 - 767520 z^7 + 79872 z^8) EllipticE[(1/2) (1 + Sqrt[z])] + (-175560 - 87780 Sqrt[z] + 1860936 z + 923153 z^(3/2) - 10014235 z^2 - 4933236 z^(5/2) + 52158876 z^3 + 64362870 z^(7/2) + 21737430 z^4 - 2179320 z^(9/2) - 9566700 z^5 + 800865 z^(11/2) + 3407157 z^6 - 186264 z^(13/2) - 767520 z^7 + 19968 z^(15/2) + 79872 z^8) EllipticK[(1/2) (1 - Sqrt[z])] - (-175560 + 87780 Sqrt[z] + 1860936 z - 923153 z^(3/2) - 10014235 z^2 + 4933236 z^(5/2) + 52158876 z^3 - 64362870 z^(7/2) + 21737430 z^4 + 2179320 z^(9/2) - 9566700 z^5 - 800865 z^(11/2) + 3407157 z^6 + 186264 z^(13/2) - 767520 z^7 - 19968 z^(15/2) + 79872 z^8) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)










Standard Form





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MathML Form







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type='integer'> 9566700 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 21737430 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 52158876 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 10014235 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1860936 </cn> <ci> z </ci> </apply> <cn type='integer'> -175560 </cn> </apply> <apply> <ci> EllipticE </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> 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type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 186264 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3407157 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 800865 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 9566700 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2179320 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 21737430 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 64362870 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Rule Form





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





2007-05-02