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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=19/4





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









  


  










Input Form





Hypergeometric2F1[7/4, 19/4, -(7/2), z] == (1/(73920 Pi^(3/2))) (((1/(-1 + z)^10) (2 (18480 - 226380 z + 1381919 z^2 - 6199347 z^3 + 36859350 z^4 + 65920030 z^5 + 3212235 z^6 - 324207 z^7 + 21216 z^8) EllipticE[(1/2) (1 - Sqrt[z])]) + (1/(-1 + z)^10) (2 (18480 - 226380 z + 1381919 z^2 - 6199347 z^3 + 36859350 z^4 + 65920030 z^5 + 3212235 z^6 - 324207 z^7 + 21216 z^8) EllipticE[(1/2) (1 + Sqrt[z])]) - (1/((-1 + Sqrt[z])^10 (1 + Sqrt[z])^9)) ((18480 - 9240 Sqrt[z] - 217140 z + 104720 z^(3/2) + 1277199 z^2 - 595287 z^(5/2) - 5604060 z^3 + 2557500 z^(7/2) + 34301850 z^4 + 20411710 z^(9/2) + 45508320 z^5 + 2983500 z^(11/2) + 228735 z^6 - 308295 z^(13/2) - 15912 z^7 + 21216 z^(15/2)) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^9 (1 + Sqrt[z])^10)) ((18480 + 9240 Sqrt[z] - 217140 z - 104720 z^(3/2) + 1277199 z^2 + 595287 z^(5/2) - 5604060 z^3 - 2557500 z^(7/2) + 34301850 z^4 - 20411710 z^(9/2) + 45508320 z^5 - 2983500 z^(11/2) + 228735 z^6 + 308295 z^(13/2) - 15912 z^7 - 21216 z^(15/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^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