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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=9/4, b>=a > For fixed z and a=9/4, b=13/4





http://functions.wolfram.com/07.23.03.al6l.01









  


  










Input Form





Hypergeometric2F1[9/4, 13/4, -(1/2), z] == (1/(30 Pi^(3/2))) (((2 Sqrt[z] (15 + 4143 z + 3957 z^2 + 77 z^3) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)^6 - (2 Sqrt[z] (15 + 4143 z + 3957 z^2 + 77 z^3) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^6 - ((-30 + 45 Sqrt[z] + 585 z + 3558 z^(3/2) + 1416 z^2 + 2541 z^(5/2) + 77 z^3) EllipticK[(1/2) (1 - Sqrt[z])])/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^5) + ((-30 - 45 Sqrt[z] + 585 z - 3558 z^(3/2) + 1416 z^2 - 2541 z^(5/2) + 77 z^3) EllipticK[(1/2) (1 + Sqrt[z])])/ ((-1 + Sqrt[z])^5 (1 + Sqrt[z])^6)) Gamma[3/4]^2)










Standard Form





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MathML Form







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</apply> <cn type='integer'> -30 </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> <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'> 5 </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'> 6 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </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