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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=1/2





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









  


  








Input Form





Hypergeometric2F1[-(17/4), 1/2, 6, z] == (512 Sqrt[2] (2 (452608 - 4653376 z + 22104420 z^2 - 65898222 z^3 + 153090015 z^4 + 311994816 z^5 - 120229312 z^6 + 39017440 z^7 - 8072064 z^8 + 776160 z^9) EllipticE[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (452608 - 4653376 z + 22104420 z^2 - 65898222 z^3 + 153090015 z^4 + 311994816 z^5 - 120229312 z^6 + 39017440 z^7 - 8072064 z^8 + 776160 z^9) EllipticE[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (-452608 + 4427072 z - 19961604 z^2 + 56573790 z^3 - 127597665 z^4 - 31307136 z^5 + 11013184 z^6 - 2481248 z^7 + 258720 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (452608 - 4653376 z + 22104420 z^2 - 65898222 z^3 + 153090015 z^4 + 311994816 z^5 - 120229312 z^6 + 39017440 z^7 - 8072064 z^8 + 776160 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (452608 - 4653376 z + 22104420 z^2 - 65898222 z^3 + 153090015 z^4 + 311994816 z^5 - 120229312 z^6 + 39017440 z^7 - 8072064 z^8 + 776160 z^9) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (452608 - 4653376 z + 22104420 z^2 - 65898222 z^3 + 153090015 z^4 + 311994816 z^5 - 120229312 z^6 + 39017440 z^7 - 8072064 z^8 + 776160 z^9) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (86274913725 Pi Sqrt[1 + Sqrt[1 - z]] z^5)








Standard Form





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MathML Form







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type='integer'> 153090015 </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'> 65898222 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 22104420 </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'> 4653376 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 452608 </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> 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Rule Form





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





2007-05-02