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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=-23/4, b>=a > For fixed z and a=-23/4, b=-19/4





http://functions.wolfram.com/07.23.03.9037.01









  


  










Input Form





Hypergeometric2F1[-(23/4), -(19/4), 7/2, z] == (1/(323467837875 Pi^(3/2) z^(5/2))) (8 (-2 (7671972 - 304960887 z + 13824254213 z^2 + 284727564485 z^3 + 1001089906505 z^4 + 1031295607339 z^5 + 325017294751 z^6 + 24338324551 z^7 + 63929775 z^8) EllipticE[(1/2) (1 - Sqrt[z])] + 2 (7671972 - 304960887 z + 13824254213 z^2 + 284727564485 z^3 + 1001089906505 z^4 + 1031295607339 z^5 + 325017294751 z^6 + 24338324551 z^7 + 63929775 z^8) EllipticE[(1/2) (1 + Sqrt[z])] + (7671972 + 3835986 Sqrt[z] - 304960887 z - 152160778 z^(3/2) + 13824254213 z^2 + 47333059970 z^(5/2) + 284727564485 z^3 + 453404905430 z^(7/2) + 1001089906505 z^4 + 1095728897830 z^(9/2) + 1031295607339 z^5 + 858904765522 z^(11/2) + 325017294751 z^6 + 212689631494 z^(13/2) + 24338324551 z^7 + 12146657250 z^(15/2) + 63929775 z^8) EllipticK[(1/2) (1 - Sqrt[z])] - (7671972 - 3835986 Sqrt[z] - 304960887 z + 152160778 z^(3/2) + 13824254213 z^2 - 47333059970 z^(5/2) + 284727564485 z^3 - 453404905430 z^(7/2) + 1001089906505 z^4 - 1095728897830 z^(9/2) + 1031295607339 z^5 - 858904765522 z^(11/2) + 325017294751 z^6 - 212689631494 z^(13/2) + 24338324551 z^7 - 12146657250 z^(15/2) + 63929775 z^8) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)










Standard Form





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MathML Form







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type='integer'> 24338324551 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 325017294751 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1031295607339 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1001089906505 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 284727564485 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 13824254213 </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'> 304960887 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 7671972 </cn> </apply> <apply> <ci> EllipticE </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 63929775 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 24338324551 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 325017294751 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1031295607339 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1001089906505 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 284727564485 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 13824254213 </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'> 304960887 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 7671972 </cn> </apply> <apply> <ci> EllipticE </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> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 63929775 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 12146657250 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 15 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 24338324551 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 212689631494 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 325017294751 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 858904765522 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1031295607339 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1095728897830 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1001089906505 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 453404905430 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 284727564485 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 47333059970 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 13824254213 </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'> 152160778 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 304960887 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 3835986 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> 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Rule Form





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





2007-05-02