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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=7/4





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









  


  










Input Form





Hypergeometric2F1[-(1/4), 7/4, -(11/2), z] == (1/(177408 Pi^(3/2))) (((1/(-1 + z)^7) (2 (-44352 + 301392 z - 870408 z^2 + 1376865 z^3 - 1270615 z^4 + 651551 z^5 - 97461 z^6 + 18564 z^7) EllipticE[(1/2) (1 - Sqrt[z])]) + (1/(-1 + z)^7) (2 (-44352 + 301392 z - 870408 z^2 + 1376865 z^3 - 1270615 z^4 + 651551 z^5 - 97461 z^6 + 18564 z^7) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^6)) ((44352 - 22176 Sqrt[z] - 279216 z + 130368 z^(3/2) + 740040 z^2 - 316470 z^(5/2) - 1060395 z^3 + 402550 z^(7/2) + 868065 z^4 - 275630 z^(9/2) - 375921 z^5 + 83538 z^(11/2) + 13923 z^6 - 18564 z^(13/2)) EllipticK[(1/2) (1 - Sqrt[z])]) - (1/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^7)) ((44352 + 22176 Sqrt[z] - 279216 z - 130368 z^(3/2) + 740040 z^2 + 316470 z^(5/2) - 1060395 z^3 - 402550 z^(7/2) + 868065 z^4 + 275630 z^(9/2) - 375921 z^5 - 83538 z^(11/2) + 13923 z^6 + 18564 z^(13/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)










Standard Form





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MathML Form







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<cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 97461 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 651551 </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'> 1270615 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1376865 </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'> 870408 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 301392 </cn> <ci> z </ci> </apply> <cn type='integer'> -44352 </cn> </apply> <apply> <ci> EllipticE </ci> 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<times /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 7 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 6 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -18564 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 13923 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 83538 </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'> 375921 </cn> <apply> <power /> 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</semantics> </math>










Rule Form





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





2007-05-02