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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=23/4





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









  


  










Input Form





Hypergeometric2F1[-(17/4), 23/4, -(9/2), z] == (1/(176964480 Pi^(3/2))) (((1/(-1 + z)^6) (4 (22120560 - 9831360 z - 12618375 z^2 - 25440107 z^3 - 83491947 z^4 - 760565421 z^5 + 5493498970 z^6 - 11579827200 z^7 + 11432472576 z^8 - 5519704064 z^9 + 1056964608 z^10) EllipticE[(1/2) (1 - Sqrt[z])]) + (1/(-1 + z)^6) (4 (22120560 - 9831360 z - 12618375 z^2 - 25440107 z^3 - 83491947 z^4 - 760565421 z^5 + 5493498970 z^6 - 11579827200 z^7 + 11432472576 z^8 - 5519704064 z^9 + 1056964608 z^10) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^5)) ((-44241120 + 22120560 Sqrt[z] - 2457840 z + 10445820 z^(3/2) + 14790930 z^2 - 2274965 z^(5/2) + 53155179 z^3 - 26851902 z^(7/2) + 193835796 z^4 - 107868453 z^(9/2) + 1628999295 z^5 - 3378184820 z^(11/2) - 7608813120 z^6 + 12157992960 z^(13/2) + 11001661440 z^7 - 16022200320 z^(15/2) - 6842744832 z^8 + 9453961216 z^(17/2) + 1585446912 z^9 - 2113929216 z^(19/2)) EllipticK[(1/2) (1 - Sqrt[z])]) - (1/((-1 + Sqrt[z])^5 (1 + Sqrt[z])^6)) ((-44241120 - 22120560 Sqrt[z] - 2457840 z - 10445820 z^(3/2) + 14790930 z^2 + 2274965 z^(5/2) + 53155179 z^3 + 26851902 z^(7/2) + 193835796 z^4 + 107868453 z^(9/2) + 1628999295 z^5 + 3378184820 z^(11/2) - 7608813120 z^6 - 12157992960 z^(13/2) + 11001661440 z^7 + 16022200320 z^(15/2) - 6842744832 z^8 - 9453961216 z^(17/2) + 1585446912 z^9 + 2113929216 z^(19/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)










Standard Form





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MathML Form







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</apply> <cn type='integer'> 6 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2113929216 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 19 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1585446912 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 9453961216 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 17 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6842744832 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 16022200320 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 15 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 11001661440 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 12157992960 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 7608813120 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3378184820 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1628999295 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 107868453 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 193835796 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 26851902 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 53155179 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2274965 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 14790930 </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'> 10445820 </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'> 2457840 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 22120560 </cn> <apply> 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Rule Form





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





2007-05-02