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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=-11/4, b>=a > For fixed z and a=-11/4, b=21/4





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









  


  










Input Form





Hypergeometric2F1[-(11/4), 21/4, 3/2, z] == (1/(129285 Pi^(3/2) Sqrt[z])) (2 (-((1/(-1 + z)) (2 (17787 - 532416 z + 2516480 z^2 - 3833856 z^3 + 1835008 z^4) EllipticE[(1/2) (1 - Sqrt[z])])) + (1/(-1 + z)) (2 (17787 - 532416 z + 2516480 z^2 - 3833856 z^3 + 1835008 z^4) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/(-1 + Sqrt[z])) ((17787 - 73536 Sqrt[z] - 458880 z + 888320 z^(3/2) + 1628160 z^2 - 2457600 z^(5/2) - 1376256 z^3 + 1835008 z^(7/2)) EllipticK[(1/2) (1 - Sqrt[z])]) - (1/(1 + Sqrt[z])) ((-17787 - 73536 Sqrt[z] + 458880 z + 888320 z^(3/2) - 1628160 z^2 - 2457600 z^(5/2) + 1376256 z^3 + 1835008 z^(7/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^2)










Standard Form





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MathML Form







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73536 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -17787 </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> <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