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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=-23/4, b>=a > For fixed z and a=-23/4, b=21/4





http://functions.wolfram.com/07.23.03.a7sj.01









  


  










Input Form





Hypergeometric2F1[-(23/4), 21/4, -(5/2), z] == (1/(132600 Pi^(3/2))) ((-((1/(-1 + z)^2) (2 Sqrt[z] (-66300 - 692835 z - 6653205 z^2 + 2689420704 z^3 - 15769958400 z^4 + 32876003328 z^5 - 29183967232 z^6 + 9395240960 z^7) EllipticE[(1/2) (1 - Sqrt[z])])) + (1/(-1 + z)^2) (2 Sqrt[z] (-66300 - 692835 z - 6653205 z^2 + 2689420704 z^3 - 15769958400 z^4 + 32876003328 z^5 - 29183967232 z^6 + 9395240960 z^7) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^2 (1 + Sqrt[z]))) ((132600 - 198900 Sqrt[z] + 1485120 z - 2177955 z^(3/2) + 14430195 z^2 - 21083400 z^(5/2) + 273156000 z^3 + 2416264704 z^(7/2) - 4920932352 z^4 - 10849026048 z^(9/2) + 17373855744 z^5 + 15502147584 z^(11/2) - 22137536512 z^6 - 7046430720 z^(13/2) + 9395240960 z^7) EllipticK[(1/2) (1 - Sqrt[z])]) - (1/(-1 - Sqrt[z] + z + z^(3/2))) ((132600 + 198900 Sqrt[z] + 1485120 z + 2177955 z^(3/2) + 14430195 z^2 + 21083400 z^(5/2) + 273156000 z^3 - 2416264704 z^(7/2) - 4920932352 z^4 + 10849026048 z^(9/2) + 17373855744 z^5 - 15502147584 z^(11/2) - 22137536512 z^6 + 7046430720 z^(13/2) + 9395240960 z^7) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^2)










Standard Form





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MathML Form







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Rule Form





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





2007-05-02