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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=-3/4





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









  


  










Input Form





Hypergeometric2F1[-(3/4), -(3/4), 11/2, z] == (1/(5128305 Pi^(3/2) z^(9/2))) (32 (-2 (1680 - 13020 z + 46249 z^2 - 106995 z^3 + 272523 z^4 + 127243 z^5) EllipticE[(1/2) (1 - Sqrt[z])] + 2 (1680 - 13020 z + 46249 z^2 - 106995 z^3 + 272523 z^4 + 127243 z^5) EllipticE[(1/2) (1 + Sqrt[z])] + (1680 + 840 Sqrt[z] - 13020 z - 6440 z^(3/2) + 46249 z^2 + 22617 z^(5/2) - 106995 z^3 - 51819 z^(7/2) + 272523 z^4 + 292867 z^(9/2) + 127243 z^5 + 69615 z^(11/2)) EllipticK[(1/2) (1 - Sqrt[z])] + (-1680 + 840 Sqrt[z] + 13020 z - 6440 z^(3/2) - 46249 z^2 + 22617 z^(5/2) + 106995 z^3 - 51819 z^(7/2) - 272523 z^4 + 292867 z^(9/2) - 127243 z^5 + 69615 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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<apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6440 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 13020 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 840 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1680 </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