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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=7/4, b>=a > For fixed z and a=7/4, b=23/4





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









  


  










Input Form





Hypergeometric2F1[7/4, 23/4, 9/2, z] == (1/(13167 Pi^(3/2) z^(7/2))) (4 ((2 Sqrt[z] (-100 + 105 z + 75 z^2 - 688 z^3 + 384 z^4) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)^3 + (2 Sqrt[z] (-100 + 105 z + 75 z^2 - 688 z^3 + 384 z^4) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^3 - (1/((-1 + Sqrt[z])^3 (1 + Sqrt[z])^2)) ((200 - 300 Sqrt[z] - 60 z + 165 z^(3/2) - 180 z^2 + 255 z^(5/2) - 400 z^3 - 288 z^(7/2) + 384 z^4) EllipticK[(1/2) (1 - Sqrt[z])]) - (1/((-1 + Sqrt[z])^2 (1 + Sqrt[z])^3)) ((200 + 300 Sqrt[z] - 60 z - 165 z^(3/2) - 180 z^2 - 255 z^(5/2) - 400 z^3 + 288 z^(7/2) + 384 z^4) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)










Standard Form





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MathML Form







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type='integer'> 180 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 165 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 60 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 300 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 200 </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> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> 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/> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 255 </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 /> <cn type='integer'> 180 </cn> <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'> 165 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 60 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 300 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 200 </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> <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