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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] > Specific values > For integer and half-integer parameters and fixed z > For fixed z and a1=1/2, a2>=1/2 > For fixed z and a1=1/2, a2=1, a3>=1 > For fixed z and a1=1/2, a2=1, a3=3 > For fixed z and a1=1/2, a2=1, a3=3, b1=7/2





http://functions.wolfram.com/07.27.03.anal.01









  


  










Input Form





HypergeometricPFQ[{1/2, 1, 3}, {7/2, 7/2}, z] == (25 I (72 Pi^2 + 504 I Sqrt[z] - 72 Pi^2 z - 404 I z^(3/2) + 27 Pi^2 z^2))/ (2048 z^(5/2)) - (675 Sqrt[1 - z] (-2 + z) ArcSin[Sqrt[z]])/ (512 z^(5/2)) - (1/(512 (-1 + z)^5 z^2)) (25 Sqrt[1 - z] (72 - 384 z + 2235 z^2 - 1269 z^3 + 1101 z^4 - 427 z^5 + 72 z^6) Log[1 - E^(I ArcSin[Sqrt[z]])]) + (1/(512 (-1 + z)^5 z^2)) (25 Sqrt[1 - z] (72 - 384 z + 2235 z^2 - 1269 z^3 + 1101 z^4 - 427 z^5 + 72 z^6) Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))]) + (225 (8 - 8 z + 3 z^2) ArcSin[Sqrt[z]] Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))])/ (512 z^(5/2)) + (1/(512 (-1 + z)^5 z^2)) (25 Sqrt[1 - z] (72 - 384 z + 2235 z^2 - 1269 z^3 + 1101 z^4 - 427 z^5 + 72 z^6) Log[1 + E^(I ArcSin[Sqrt[z]])]) + (225 I (8 - 8 z + 3 z^2) PolyLog[2, -E^(I ArcSin[Sqrt[z]])])/ (512 z^(5/2)) - (225 I (8 - 8 z + 3 z^2) PolyLog[2, E^(I ArcSin[Sqrt[z]])])/(512 z^(5/2))










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