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





http://functions.wolfram.com/07.23.03.acy5.01









  


  










Input Form





Hypergeometric2F1[-(11/4), -(11/4), 7/2, z] == (1/(46154745 Pi^(3/2) z^(5/2))) (8 (-2 (10164 - 185493 z + 3350732 z^2 + 21279762 z^3 + 15909192 z^4 + 1578683 z^5) EllipticE[(1/2) (1 - Sqrt[z])] + 2 (10164 - 185493 z + 3350732 z^2 + 21279762 z^3 + 15909192 z^4 + 1578683 z^5) EllipticE[(1/2) (1 + Sqrt[z])] + (10164 + 5082 Sqrt[z] - 185493 z - 92323 z^(3/2) + 3350732 z^2 + 7437192 z^(5/2) + 21279762 z^3 + 22520502 z^(7/2) + 15909192 z^4 + 11306822 z^(9/2) + 1578683 z^5 + 765765 z^(11/2)) EllipticK[(1/2) (1 - Sqrt[z])] + (-10164 + 5082 Sqrt[z] + 185493 z - 92323 z^(3/2) - 3350732 z^2 + 7437192 z^(5/2) - 21279762 z^3 + 22520502 z^(7/2) - 15909192 z^4 + 11306822 z^(9/2) - 1578683 z^5 + 765765 z^(11/2)) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)










Standard Form





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MathML Form







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<times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 92323 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 185493 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 5082 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -10164 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02