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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=-19/4, b>=a > For fixed z and a=-19/4, b=21/4





http://functions.wolfram.com/07.23.03.a9uf.01









  


  










Input Form





Hypergeometric2F1[-(19/4), 21/4, -(7/2), z] == (1/(53040 Pi^(3/2))) ((-((1/(-1 + z)^4) (8 Sqrt[z] (-6630 - 23205 z - 81549 z^2 - 385203 z^3 + 72187755 z^4 - 289743360 z^5 + 440330240 z^6 - 297795584 z^7 + 75497472 z^8) EllipticE[(1/2) (1 - Sqrt[z])])) + (1/(-1 + z)^4) (8 Sqrt[z] (-6630 - 23205 z - 81549 z^2 - 385203 z^3 + 72187755 z^4 - 289743360 z^5 + 440330240 z^6 - 297795584 z^7 + 75497472 z^8) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^4 (1 + Sqrt[z])^3)) ((53040 - 79560 Sqrt[z] + 225420 z - 318240 z^(3/2) + 825435 z^2 - 1151631 z^(5/2) + 3720093 z^3 - 5260905 z^(7/2) + 38520300 z^4 + 250230720 z^(9/2) - 453857280 z^5 - 705116160 z^(11/2) + 1073192960 z^6 + 688128000 z^(13/2) - 964689920 z^7 - 226492416 z^(15/2) + 301989888 z^8) EllipticK[(1/2) (1 - Sqrt[z])]) - (1/((-1 + Sqrt[z])^3 (1 + Sqrt[z])^4)) ((53040 + 79560 Sqrt[z] + 225420 z + 318240 z^(3/2) + 825435 z^2 + 1151631 z^(5/2) + 3720093 z^3 + 5260905 z^(7/2) + 38520300 z^4 - 250230720 z^(9/2) - 453857280 z^5 + 705116160 z^(11/2) + 1073192960 z^6 - 688128000 z^(13/2) - 964689920 z^7 + 226492416 z^(15/2) + 301989888 z^8) 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