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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=1/4, b>=a > For fixed z and a=1/4, b=21/4





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









  


  










Input Form





Hypergeometric2F1[1/4, 21/4, -(7/2), z] == (1/(53040 Pi^(3/2))) (((1/(-1 + z)^9) (2 Sqrt[z] (-26520 + 238680 z - 972621 z^2 + 2437188 z^3 + 10974810 z^4 - 6241620 z^5 + 2526755 z^6 - 615648 z^7 + 67584 z^8) EllipticE[(1/2) (1 - Sqrt[z])]) - (1/(-1 + z)^9) (2 Sqrt[z] (-26520 + 238680 z - 972621 z^2 + 2437188 z^3 + 10974810 z^4 - 6241620 z^5 + 2526755 z^6 - 615648 z^7 + 67584 z^8) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^9 (1 + Sqrt[z])^8)) ((-53040 + 79560 Sqrt[z] + 437580 z - 676260 z^(3/2) - 1621035 z^2 + 2593656 z^(5/2) + 3688932 z^3 - 6126120 z^(7/2) - 7657650 z^4 - 3317160 z^(9/2) + 4721640 z^5 + 1519980 z^(11/2) - 2110955 z^6 - 415800 z^(13/2) + 564960 z^7 + 50688 z^(15/2) - 67584 z^8) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^8 (1 + Sqrt[z])^9)) ((53040 + 79560 Sqrt[z] - 437580 z - 676260 z^(3/2) + 1621035 z^2 + 2593656 z^(5/2) - 3688932 z^3 - 6126120 z^(7/2) + 7657650 z^4 - 3317160 z^(9/2) - 4721640 z^5 + 1519980 z^(11/2) + 2110955 z^6 - 415800 z^(13/2) - 564960 z^7 + 50688 z^(15/2) + 67584 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