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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=-17/4





http://functions.wolfram.com/07.23.03.aa7l.01









  


  










Input Form





Hypergeometric2F1[-(17/4), -(17/4), 11/2, z] == (8 (8 Sqrt[z] (-1465230 + 31502445 z - 373340604 z^2 + 3761098887 z^3 + 1084536314190 z^4 + 3307335901275 z^5 + 2466911129200 z^6 + 490265521681 z^7 + 17697218092 z^8) EllipticE[(1/2) (1 - Sqrt[z])] + 8 Sqrt[z] (-1465230 + 31502445 z - 373340604 z^2 + 3761098887 z^3 + 1084536314190 z^4 + 3307335901275 z^5 + 2466911129200 z^6 + 490265521681 z^7 + 17697218092 z^8) EllipticE[(1/2) (1 + Sqrt[z])] - (11721840 - 5860920 Sqrt[z] - 260810940 z + 126009780 z^(3/2) + 3174420795 z^2 - 1493362416 z^(5/2) - 32301141873 z^3 + 15044395548 z^(7/2) + 526774361295 z^4 + 4338145256760 z^(9/2) + 6759597924555 z^5 + 13229343605100 z^(11/2) + 13459643108065 z^6 + 9867644516800 z^(13/2) + 7563703414045 z^7 + 1961062086724 z^(15/2) + 1169191066597 z^8 + 70788872368 z^(17/2) + 31121455365 z^9) EllipticK[(1/2) (1 - Sqrt[z])] + (11721840 + 5860920 Sqrt[z] - 260810940 z - 126009780 z^(3/2) + 3174420795 z^2 + 1493362416 z^(5/2) - 32301141873 z^3 - 15044395548 z^(7/2) + 526774361295 z^4 - 4338145256760 z^(9/2) + 6759597924555 z^5 - 13229343605100 z^(11/2) + 13459643108065 z^6 - 9867644516800 z^(13/2) + 7563703414045 z^7 - 1961062086724 z^(15/2) + 1169191066597 z^8 - 70788872368 z^(17/2) + 31121455365 z^9) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[1/4]^2)/ (146893128501735 Pi^(3/2) z^(9/2))










Standard Form





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MathML Form







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





2007-05-02