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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=21/4





http://functions.wolfram.com/07.23.03.ah0x.01









  


  








Input Form





Hypergeometric2F1[-(3/4), 21/4, -(9/2), z] == (1/(318240 Pi^(3/2))) (((1/(-1 + z)^9) (2 Sqrt[z] (-159120 + 1233180 z - 3995901 z^2 + 6640608 z^3 - 4594590 z^4 + 23423400 z^5 - 23579325 z^6 + 12619332 z^7 - 3649536 z^8 + 450560 z^9) EllipticE[(1/2) (1 - Sqrt[z])]) - (1/(-1 + z)^9) (2 Sqrt[z] (-159120 + 1233180 z - 3995901 z^2 + 6640608 z^3 - 4594590 z^4 + 23423400 z^5 - 23579325 z^6 + 12619332 z^7 - 3649536 z^8 + 450560 z^9) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^9 (1 + Sqrt[z])^8)) ((-318240 + 477360 Sqrt[z] + 2227680 z - 3460860 z^(3/2) - 6344910 z^2 + 10340811 z^(5/2) + 8674692 z^3 - 15315300 z^(7/2) - 3063060 z^4 + 7657650 z^(9/2) - 12252240 z^5 - 11171160 z^(11/2) + 16306290 z^6 + 7273035 z^(13/2) - 10188420 z^7 - 2430912 z^(15/2) + 3311616 z^8 + 337920 z^(17/2) - 450560 z^9) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^8 (1 + Sqrt[z])^9)) ((318240 + 477360 Sqrt[z] - 2227680 z - 3460860 z^(3/2) + 6344910 z^2 + 10340811 z^(5/2) - 8674692 z^3 - 15315300 z^(7/2) + 3063060 z^4 + 7657650 z^(9/2) + 12252240 z^5 - 11171160 z^(11/2) - 16306290 z^6 + 7273035 z^(13/2) + 10188420 z^7 - 2430912 z^(15/2) - 3311616 z^8 + 337920 z^(17/2) + 450560 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='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 11171160 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 12252240 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 7657650 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3063060 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 15315300 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8674692 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 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Date Added to functions.wolfram.com (modification date)





2007-05-02