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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=-13/4, b>=a > For fixed z and a=-13/4, b=11/4





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









  


  










Input Form





Hypergeometric2F1[-(13/4), 11/4, -(11/2), z] == (1/(413952 Pi^(3/2))) (((1/(-1 + z)^5) (2 (-103488 + 336336 z - 314776 z^2 + 26565 z^3 + 16170 z^4 + 19789 z^5 + 62412 z^6 - 110592 z^7 + 40960 z^8) EllipticE[(1/2) (1 - Sqrt[z])]) + (1/(-1 + z)^5) (2 (-103488 + 336336 z - 314776 z^2 + 26565 z^3 + 16170 z^4 + 19789 z^5 + 62412 z^6 - 110592 z^7 + 40960 z^8) EllipticE[(1/2) (1 + Sqrt[z])]) - (1/((-1 + Sqrt[z])^5 (1 + Sqrt[z])^4)) ((-103488 + 51744 Sqrt[z] + 284592 z - 120736 z^(3/2) - 194040 z^2 + 48510 z^(5/2) - 21945 z^3 + 27720 z^(7/2) - 11550 z^4 + 17710 z^(9/2) + 2079 z^5 + 7308 z^(11/2) + 55104 z^6 - 79872 z^(13/2) - 30720 z^7 + 40960 z^(15/2)) EllipticK[(1/2) (1 - Sqrt[z])]) - (1/((-1 + Sqrt[z])^4 (1 + Sqrt[z])^5)) ((103488 + 51744 Sqrt[z] - 284592 z - 120736 z^(3/2) + 194040 z^2 + 48510 z^(5/2) + 21945 z^3 + 27720 z^(7/2) + 11550 z^4 + 17710 z^(9/2) - 2079 z^5 + 7308 z^(11/2) - 55104 z^6 - 79872 z^(13/2) + 30720 z^7 + 40960 z^(15/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)










Standard Form





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MathML Form







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type='integer'> 7308 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2079 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 17710 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 11550 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 27720 </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'> 21945 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 48510 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 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Rule Form





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





2007-05-02