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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=-21/4, b>=a > For fixed z and a=-21/4, b=-3/2





http://functions.wolfram.com/07.23.03.a8db.01









  


  








Input Form





Hypergeometric2F1[-(21/4), -(3/2), 2, z] == (1/(1740375 Pi Sqrt[1 + Sqrt[1 - z]] z)) (Sqrt[2] (-2 (-55692 - 6659174 z - 18516355 z^2 - 3408000 z^3 + 555200 z^4 - 87584 z^5 + 7392 z^6) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (-55692 - 6659174 z - 18516355 z^2 - 3408000 z^3 + 555200 z^4 - 87584 z^5 + 7392 z^6) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (55692 + 3206270 z + 5987645 z^2 + 163200 z^3 - 27200 z^4 + 2464 z^5) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (-55692 - 6659174 z - 18516355 z^2 - 3408000 z^3 + 555200 z^4 - 87584 z^5 + 7392 z^6) EllipticK[1/2 - (1 - z)^(1/4)/ (1 + Sqrt[1 - z])] + (1 - z)^(1/4) (-55692 - 6659174 z - 18516355 z^2 - 3408000 z^3 + 555200 z^4 - 87584 z^5 + 7392 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (-55692 - 6659174 z - 18516355 z^2 - 3408000 z^3 + 555200 z^4 - 87584 z^5 + 7392 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))








Standard Form





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MathML Form







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<apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 7392 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 87584 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 555200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3408000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 18516355 </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'> 6659174 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -55692 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> 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Rule Form





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





2007-05-02