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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=19/4, b>=a > For fixed z and a=19/4, b=19/4





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









  


  










Input Form





Hypergeometric2F1[19/4, 19/4, 5/2, z] == (1/(88935 Pi^(3/2) z^(3/2))) ((-((2 Sqrt[z] (45 + 20985 z + 37767 z^2 + 6739 z^3) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)^7) - (2 Sqrt[z] (45 + 20985 z + 37767 z^2 + 6739 z^3) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^7 + (1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^6)) ((-90 + 135 Sqrt[z] + 2430 z + 18555 z^(3/2) + 10770 z^2 + 26997 z^(5/2) + 3274 z^3 + 3465 z^(7/2)) EllipticK[(1/2) (1 - Sqrt[z])]) - (1/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^7)) ((90 + 135 Sqrt[z] - 2430 z + 18555 z^(3/2) - 10770 z^2 + 26997 z^(5/2) - 3274 z^3 + 3465 z^(7/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)










Standard Form





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MathML Form







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<power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 18555 </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'> 2430 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 135 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 90 </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