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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=-3/4, b>=a > For fixed z and a=-3/4, b=17/4





http://functions.wolfram.com/07.23.03.agx7.01









  


  










Input Form





Hypergeometric2F1[-(3/4), 17/4, -(1/2), z] == (1/(390 Pi^(3/2))) (((2 Sqrt[z] (195 - 4950 z + 9843 z^2 - 7520 z^3 + 2048 z^4) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)^4 - (2 Sqrt[z] (195 - 4950 z + 9843 z^2 - 7520 z^3 + 2048 z^4) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^4 + (1/((-1 + Sqrt[z])^4 (1 + Sqrt[z])^3)) ((390 - 585 Sqrt[z] + 1365 z + 3585 z^(3/2) - 5595 z^2 - 4248 z^(5/2) + 5984 z^3 + 1536 z^(7/2) - 2048 z^4) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^3 (1 + Sqrt[z])^4)) ((-390 - 585 Sqrt[z] - 1365 z + 3585 z^(3/2) + 5595 z^2 - 4248 z^(5/2) - 5984 z^3 + 1536 z^(7/2) + 2048 z^4) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^2)










Standard Form





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MathML Form







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<cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4248 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5595 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3585 </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'> 1365 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 585 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -390 </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> <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