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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=15/4





http://functions.wolfram.com/07.23.03.a8rn.01









  


  










Input Form





Hypergeometric2F1[-(21/4), 15/4, -(9/2), z] == (1/(88704 Pi^(3/2))) (((1/(-1 + z)^3) (2 (-22176 - 33264 z - 60522 z^2 - 136521 z^3 - 437085 z^4 - 3420032 z^5 + 17958912 z^6 - 22216704 z^7 + 8388608 z^8) EllipticE[(1/2) (1 - Sqrt[z])]) + (1/(-1 + z)^3) (2 (-22176 - 33264 z - 60522 z^2 - 136521 z^3 - 437085 z^4 - 3420032 z^5 + 17958912 z^6 - 22216704 z^7 + 8388608 z^8) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^3 (1 + Sqrt[z])^2)) ((22176 - 11088 Sqrt[z] + 44352 z - 26796 z^(3/2) + 87318 z^2 - 55209 z^(5/2) + 191730 z^3 - 119955 z^(7/2) + 557040 z^4 - 330880 z^(9/2) + 3750912 z^5 - 6998016 z^(11/2) - 10960896 z^6 + 15925248 z^(13/2) + 6291456 z^7 - 8388608 z^(15/2)) EllipticK[(1/2) (1 - Sqrt[z])]) - (1/((-1 + Sqrt[z])^2 (1 + Sqrt[z])^3)) ((22176 + 11088 Sqrt[z] + 44352 z + 26796 z^(3/2) + 87318 z^2 + 55209 z^(5/2) + 191730 z^3 + 119955 z^(7/2) + 557040 z^4 + 330880 z^(9/2) + 3750912 z^5 + 6998016 z^(11/2) - 10960896 z^6 - 15925248 z^(13/2) + 6291456 z^7 + 8388608 z^(15/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)










Standard Form





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MathML Form







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type='integer'> 6291456 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 15925248 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 10960896 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6998016 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3750912 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 330880 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 557040 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Rule Form





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





2007-05-02