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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.aazb.01









  


  










Input Form





Hypergeometric2F1[-(17/4), 23/4, 3/2, z] == (1/(192633210 Pi^(3/2))) ((8 (11764845 - 181040640 z + 734877696 z^2 - 1086324736 z^3 + 528482304 z^4) EllipticE[(1/2) (1 - Sqrt[z])] + 8 (11764845 - 181040640 z + 734877696 z^2 - 1086324736 z^3 + 528482304 z^4) EllipticE[(1/2) (1 + Sqrt[z])] - (1/Sqrt[z]) ((2197845 + 47059380 Sqrt[z] - 86362560 z - 724162560 z^(3/2) + 509859840 z^2 + 2939510784 z^(5/2) - 937689088 z^3 - 4345298944 z^(7/2) + 528482304 z^4 + 2113929216 z^(9/2)) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/Sqrt[z]) ((2197845 - 47059380 Sqrt[z] - 86362560 z + 724162560 z^(3/2) + 509859840 z^2 - 2939510784 z^(5/2) - 937689088 z^3 + 4345298944 z^(7/2) + 528482304 z^4 - 2113929216 z^(9/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)










Standard Form





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MathML Form







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</apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02