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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=-7/4, b>=a > For fixed z and a=-7/4, b=21/4





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









  


  










Input Form





Hypergeometric2F1[-(7/4), 21/4, -(7/2), z] == (1/(53040 Pi^(3/2))) (((1/(-1 + z)^7) (2 Sqrt[z] (-26520 + 106080 z - 97461 z^2 - 78897 z^3 + 1837689 z^4 - 3420123 z^5 + 2860928 z^6 - 1181696 z^7 + 196608 z^8) EllipticE[(1/2) (1 - Sqrt[z])]) - (1/(-1 + z)^7) (2 Sqrt[z] (-26520 + 106080 z - 97461 z^2 - 78897 z^3 + 1837689 z^4 - 3420123 z^5 + 2860928 z^6 - 1181696 z^7 + 196608 z^8) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^6)) ((-53040 + 79560 Sqrt[z] + 172380 z - 278460 z^(3/2) - 69615 z^2 + 167076 z^(5/2) - 199563 z^3 + 278460 z^(7/2) - 580125 z^4 - 1257564 z^(9/2) + 1951467 z^5 + 1468656 z^(11/2) - 2108288 z^6 - 752640 z^(13/2) + 1034240 z^7 + 147456 z^(15/2) - 196608 z^8) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^7)) ((53040 + 79560 Sqrt[z] - 172380 z - 278460 z^(3/2) + 69615 z^2 + 167076 z^(5/2) + 199563 z^3 + 278460 z^(7/2) + 580125 z^4 - 1257564 z^(9/2) - 1951467 z^5 + 1468656 z^(11/2) + 2108288 z^6 - 752640 z^(13/2) - 1034240 z^7 + 147456 z^(15/2) + 196608 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