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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=15/4





http://functions.wolfram.com/07.23.03.ag6j.01









  


  










Input Form





Hypergeometric2F1[-(5/4), 15/4, -(1/2), z] == (1/(1848 Pi^(3/2))) (((2 (-462 - 3003 z + 14281 z^2 - 16800 z^3 + 6144 z^4) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)^3 + (2 (-462 - 3003 z + 14281 z^2 - 16800 z^3 + 6144 z^4) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^3 + (1/((-1 + Sqrt[z])^3 (1 + Sqrt[z])^2)) ((462 - 231 Sqrt[z] + 3234 z - 5857 z^(3/2) - 8424 z^2 + 12192 z^(5/2) + 4608 z^3 - 6144 z^(7/2)) EllipticK[(1/2) (1 - Sqrt[z])]) - (1/((-1 + Sqrt[z])^2 (1 + Sqrt[z])^3)) ((462 + 231 Sqrt[z] + 3234 z + 5857 z^(3/2) - 8424 z^2 - 12192 z^(5/2) + 4608 z^3 + 6144 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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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