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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=-17/4, b>=a > For fixed z and a=-17/4, b=-13/4





http://functions.wolfram.com/07.23.03.aa9n.01









  


  










Input Form





Hypergeometric2F1[-(17/4), -(13/4), 4, z] == (1/(1766480625 Pi z^3)) (256 (2 (1248 - 28197 z + 462150 z^2 + 32826325 z^3 + 92661300 z^4 + 56073333 z^5 + 6745478 z^6 + 20475 z^7) EllipticE[(1/2) (1 - Sqrt[1 - z])] - Sqrt[1 - z] (1248 - 27885 z + 455325 z^2 + 19136350 z^3 + 47253850 z^4 + 25043743 z^5 + 2518425 z^6) EllipticK[(1/2) (1 - Sqrt[1 - z])] - (1248 - 28197 z + 462150 z^2 + 32826325 z^3 + 92661300 z^4 + 56073333 z^5 + 6745478 z^6 + 20475 z^7) EllipticK[(1/2) (1 - Sqrt[1 - z])]))










Standard Form





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MathML Form







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</cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2518425 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 25043743 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 47253850 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 19136350 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 455325 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 27885 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 1248 </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 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Rule Form





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





2007-05-02