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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=-23/4, b>=a > For fixed z and a=-23/4, b=-3/4





http://functions.wolfram.com/07.23.03.9385.01









  


  










Input Form





Hypergeometric2F1[-(23/4), -(3/4), 7/2, z] == (1/(1443467025 Pi^(3/2) z^(5/2))) (8 (-2 (403788 - 7167237 z + 116862977 z^2 + 537271966 z^3 + 73165950 z^4 - 20309289 z^5 + 5267301 z^6 - 932256 z^7 + 79872 z^8) EllipticE[(1/2) (1 - Sqrt[z])] + 2 (403788 - 7167237 z + 116862977 z^2 + 537271966 z^3 + 73165950 z^4 - 20309289 z^5 + 5267301 z^6 - 932256 z^7 + 79872 z^8) EllipticE[(1/2) (1 + Sqrt[z])] + (403788 + 201894 Sqrt[z] - 7167237 z - 3566794 z^(3/2) + 116862977 z^2 + 238574644 z^(5/2) + 537271966 z^3 + 473126940 z^(7/2) + 73165950 z^4 - 4740450 z^(9/2) - 20309289 z^5 + 1254318 z^(11/2) + 5267301 z^6 - 227448 z^(13/2) - 932256 z^7 + 19968 z^(15/2) + 79872 z^8) EllipticK[(1/2) (1 - Sqrt[z])] - (403788 - 201894 Sqrt[z] - 7167237 z + 3566794 z^(3/2) + 116862977 z^2 - 238574644 z^(5/2) + 537271966 z^3 - 473126940 z^(7/2) + 73165950 z^4 + 4740450 z^(9/2) - 20309289 z^5 - 1254318 z^(11/2) + 5267301 z^6 + 227448 z^(13/2) - 932256 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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<power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 20309289 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 73165950 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 537271966 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 116862977 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 7167237 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 403788 </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> 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type='integer'> 932256 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 227448 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5267301 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1254318 </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'> 20309289 </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'> 4740450 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 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Rule Form





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





2007-05-02