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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.aisp.01









  


  










Input Form





Hypergeometric2F1[3/4, 3/4, -(7/2), z] == (1/(6720 Pi^(3/2))) ((-((2 (1680 - 8460 z + 17341 z^2 - 18806 z^3 + 14389 z^4) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)^5) - (2 (1680 - 8460 z + 17341 z^2 - 18806 z^3 + 14389 z^4) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^5 + (1/((-1 + Sqrt[z])^5 (1 + Sqrt[z])^4)) ((1680 - 840 Sqrt[z] - 7620 z + 3460 z^(3/2) + 13881 z^2 - 5528 z^(5/2) - 13278 z^3 + 4444 z^(7/2) + 9945 z^4) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^4 (1 + Sqrt[z])^5)) ((-1680 - 840 Sqrt[z] + 7620 z + 3460 z^(3/2) - 13881 z^2 - 5528 z^(5/2) + 13278 z^3 + 4444 z^(7/2) - 9945 z^4) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)










Standard Form





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MathML Form







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</apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 13881 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3460 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 7620 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 840 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </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> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 1 <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