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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=5/4, b>=a > For fixed z and a=5/4, b=17/4





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









  


  










Input Form





Hypergeometric2F1[5/4, 17/4, -(7/2), z] == (1/(21840 Pi^(3/2))) (((1/(-1 + z)^9) (2 Sqrt[z] (-10920 + 110760 z - 540891 z^2 + 1849692 z^3 + 53474166 z^4 + 4371444 z^5 - 580811 z^6 + 46816 z^7) EllipticE[(1/2) (1 - Sqrt[z])]) - (1/(-1 + z)^9) (2 Sqrt[z] (-10920 + 110760 z - 540891 z^2 + 1849692 z^3 + 53474166 z^4 + 4371444 z^5 - 580811 z^6 + 46816 z^7) EllipticE[(1/2) (1 + Sqrt[z])]) - (1/((-1 + Sqrt[z])^9 (1 + Sqrt[z])^8)) ((21840 - 32760 Sqrt[z] - 205140 z + 315900 z^(3/2) + 929565 z^2 - 1470456 z^(5/2) - 3016572 z^3 + 4866264 z^(7/2) + 13481598 z^4 + 39992568 z^(9/2) + 3967656 z^5 + 403788 z^(11/2) - 545699 z^6 - 35112 z^(13/2) + 46816 z^7) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^8 (1 + Sqrt[z])^9)) ((21840 + 32760 Sqrt[z] - 205140 z - 315900 z^(3/2) + 929565 z^2 + 1470456 z^(5/2) - 3016572 z^3 - 4866264 z^(7/2) + 13481598 z^4 - 39992568 z^(9/2) + 3967656 z^5 - 403788 z^(11/2) - 545699 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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<ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 110760 </cn> <ci> z </ci> </apply> <cn type='integer'> -10920 </cn> </apply> <apply> <ci> EllipticE </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 9 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 46816 </cn> <apply> <power 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</cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <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'> 8 </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'> 9 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <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'> 545699 </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'> 403788 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3967656 </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'> 39992568 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 13481598 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> 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Rule Form





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





2007-05-02