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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=1/4, b>=a > For fixed z and a=1/4, b=13/4





http://functions.wolfram.com/07.23.03.ai9q.01









  


  










Input Form





Hypergeometric2F1[1/4, 13/4, -(9/2), z] == (1/(30240 Pi^(3/2))) (((1/(-1 + z)^8) (2 Sqrt[z] (15120 - 118020 z + 404361 z^2 - 801180 z^3 + 1037046 z^4 + 1650264 z^5 - 399399 z^6 + 46816 z^7) EllipticE[(1/2) (1 - Sqrt[z])]) - (1/(-1 + z)^8) (2 Sqrt[z] (15120 - 118020 z + 404361 z^2 - 801180 z^3 + 1037046 z^4 + 1650264 z^5 - 399399 z^6 + 46816 z^7) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^8 (1 + Sqrt[z])^7)) ((30240 - 45360 Sqrt[z] - 213360 z + 331380 z^(3/2) + 650970 z^2 - 1055331 z^(5/2) - 1128717 z^3 + 1929897 z^(7/2) + 1267179 z^4 - 2304225 z^(9/2) - 1382535 z^5 - 267729 z^(11/2) + 364287 z^6 + 35112 z^(13/2) - 46816 z^7) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^8)) ((-30240 - 45360 Sqrt[z] + 213360 z + 331380 z^(3/2) - 650970 z^2 - 1055331 z^(5/2) + 1128717 z^3 + 1929897 z^(7/2) - 1267179 z^4 - 2304225 z^(9/2) + 1382535 z^5 - 267729 z^(11/2) - 364287 z^6 + 35112 z^(13/2) + 46816 z^7) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^2)










Standard Form





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MathML Form







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</apply> <apply> <times /> <cn type='integer'> 35112 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 364287 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 267729 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1382535 </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'> 2304225 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1267179 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> 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<apply> <plus /> <apply> <times /> <cn type='integer'> 46816 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 35112 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 364287 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 267729 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1382535 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2304225 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> </apply> <apply> 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Rule Form





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





2007-05-02