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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=-3/4, b>=a > For fixed z and a=-3/4, b=5/4





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









  


  










Input Form





Hypergeometric2F1[-(3/4), 5/4, -(11/2), z] == (1/(73920 Pi^(3/2))) (((1/(-1 + z)^6) (4 Sqrt[z] (18480 - 100800 z + 221949 z^2 - 245991 z^3 + 134157 z^4 - 21945 z^5 + 14630 z^6) EllipticE[(1/2) (1 - Sqrt[z])]) - (1/(-1 + z)^6) (4 Sqrt[z] (18480 - 100800 z + 221949 z^2 - 245991 z^3 + 134157 z^4 - 21945 z^5 + 14630 z^6) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^5)) ((73920 - 110880 Sqrt[z] - 347760 z + 549360 z^(3/2) + 632520 z^2 - 1076418 z^(5/2) - 532191 z^3 + 1024173 z^(7/2) + 170586 z^4 - 438900 z^(9/2) + 21945 z^5 + 21945 z^(11/2) - 29260 z^6) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^5 (1 + Sqrt[z])^6)) ((-73920 - 110880 Sqrt[z] + 347760 z + 549360 z^(3/2) - 632520 z^2 - 1076418 z^(5/2) + 532191 z^3 + 1024173 z^(7/2) - 170586 z^4 - 438900 z^(9/2) - 21945 z^5 + 21945 z^(11/2) + 29260 z^6) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^2)










Standard Form





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MathML Form







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<cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 21945 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 21945 </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'> 438900 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 170586 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1024173 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 532191 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 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Rule Form





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





2007-05-02