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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=-5/4, b>=a > For fixed z and a=-5/4, b=3/4





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









  


  










Input Form





Hypergeometric2F1[-(5/4), 3/4, -(9/2), z] == (1/(8064 Pi^(3/2))) (((4 (1008 - 3696 z + 4809 z^2 - 2380 z^3 + 117 z^4 + 78 z^5) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)^4 + (4 (1008 - 3696 z + 4809 z^2 - 2380 z^3 + 117 z^4 + 78 z^5) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^4 + (1/((-1 + Sqrt[z])^4 (1 + Sqrt[z])^3)) ((-2016 + 1008 Sqrt[z] + 6384 z - 2772 z^(3/2) - 6846 z^2 + 2303 z^(5/2) + 2457 z^3 - 351 z^(7/2) + 117 z^4 - 156 z^(9/2)) EllipticK[(1/2) (1 - Sqrt[z])]) - (1/((-1 + Sqrt[z])^3 (1 + Sqrt[z])^4)) ((-2016 - 1008 Sqrt[z] + 6384 z + 2772 z^(3/2) - 6846 z^2 - 2303 z^(5/2) + 2457 z^3 + 351 z^(7/2) + 117 z^4 + 156 z^(9/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)










Standard Form





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MathML Form







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<sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 6384 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 1008 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -2016 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <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'> 3 </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'> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 156 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 117 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 351 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2457 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2303 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> 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</annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02