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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=-15/4, b>=a > For fixed z and a=-15/4, b=21/4





http://functions.wolfram.com/07.23.03.abt4.01









  


  










Input Form





Hypergeometric2F1[-(15/4), 21/4, -(9/2), z] == (1/(318240 Pi^(3/2))) (((1/(-1 + z)^6) (2 Sqrt[z] (159120 - 198900 z - 141219 z^2 - 167739 z^3 - 344097 z^4 + 26476515 z^5 - 72816000 z^6 + 80971776 z^7 - 41877504 z^8 + 8388608 z^9) EllipticE[(1/2) (1 - Sqrt[z])]) - (1/(-1 + z)^6) (2 Sqrt[z] (159120 - 198900 z - 141219 z^2 - 167739 z^3 - 344097 z^4 + 26476515 z^5 - 72816000 z^6 + 80971776 z^7 - 41877504 z^8 + 8388608 z^9) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^5)) ((318240 - 477360 Sqrt[z] - 159120 z + 358020 z^(3/2) - 377910 z^2 + 519129 z^(5/2) - 615927 z^3 + 783666 z^(7/2) - 1177488 z^4 + 1521585 z^(9/2) - 5201235 z^5 - 21275280 z^(11/2) + 35168640 z^6 + 37647360 z^(13/2) - 55265280 z^7 - 25706496 z^(15/2) + 35586048 z^8 + 6291456 z^(17/2) - 8388608 z^9) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^5 (1 + Sqrt[z])^6)) ((-318240 - 477360 Sqrt[z] + 159120 z + 358020 z^(3/2) + 377910 z^2 + 519129 z^(5/2) + 615927 z^3 + 783666 z^(7/2) + 1177488 z^4 + 1521585 z^(9/2) + 5201235 z^5 - 21275280 z^(11/2) - 35168640 z^6 + 37647360 z^(13/2) + 55265280 z^7 - 25706496 z^(15/2) - 35586048 z^8 + 6291456 z^(17/2) + 8388608 z^9) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^2)










Standard Form





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MathML Form







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type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 615927 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 519129 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 377910 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 358020 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 159120 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 477360 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -318240 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> 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Rule Form





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





2007-05-02