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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=-11/2, b>=a > For fixed z and a=-11/2, b=-9/4





http://functions.wolfram.com/07.23.03.a7xx.01









  


  










Input Form





Hypergeometric2F1[-(11/2), -(9/4), 6, z] == (8 Sqrt[2] (2 (1441792 - 27258880 z + 268187392 z^2 - 1987138560 z^3 + 15855593600 z^4 + 458649839424 z^5 + 714579955600 z^6 + 209374577744 z^7 + 1042744300 z^8 - 61205950 z^9 + 2403375 z^10) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (1441792 - 27258880 z + 268187392 z^2 - 1987138560 z^3 + 15855593600 z^4 + 458649839424 z^5 + 714579955600 z^6 + 209374577744 z^7 + 1042744300 z^8 - 61205950 z^9 + 2403375 z^10) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1441792 - 27258880 z + 268187392 z^2 - 1987138560 z^3 + 15855593600 z^4 + 458649839424 z^5 + 714579955600 z^6 + 209374577744 z^7 + 1042744300 z^8 - 61205950 z^9 + 2403375 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (1441792 - 27258880 z + 268187392 z^2 - 1987138560 z^3 + 15855593600 z^4 + 458649839424 z^5 + 714579955600 z^6 + 209374577744 z^7 + 1042744300 z^8 - 61205950 z^9 + 2403375 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (1441792 - 27258880 z + 268187392 z^2 - 1987138560 z^3 + 15855593600 z^4 + 458649839424 z^5 + 714579955600 z^6 + 209374577744 z^7 + 1042744300 z^8 - 61205950 z^9 + 2403375 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (-1441792 + 26537984 z - 255143680 z^2 + 1863600640 z^3 - 14961654400 z^4 - 193884957504 z^5 - 218784380752 z^6 - 40840711600 z^7 + 995317700 z^8 - 59283250 z^9 + 2403375 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (1087892981175 Pi Sqrt[1 + Sqrt[1 - z]] z^5)










Standard Form





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MathML Form







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</apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 1087892981175 </cn> <pi /> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










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





2007-05-02