Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ac7u)

HypergeometricPFQ

$Mathematica Notation$

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=-5/2, a₂>=-5/2

For fixed z and a₁=-5/2, a₂=2, a₃>=2

For fixed z and a₁=-5/2, a₂=2, a₃=2

For fixed z and a₁=-5/2, a₂=2, a₃=2, b₁=-3/2

http://functions.wolfram.com/07.27.03.ac7u.01

Input Form

HypergeometricPFQ[{-(5/2), 2, 2}, {-(3/2), 5/2}, z] == -((I (2880 I + 4704 I z + 9800 I z^2 + 44100 I z^3 + 11025 Pi^2 z^(7/2)))/ (6144 z)) + (5 Sqrt[1 - z] (48 - 56 z - 98 z^2 - 245 z^3 + 735 z^4) ArcSin[Sqrt[z]])/(512 (-1 + z) z^(3/2)) - (1/(24576 (-1 + z)^8)) (Sqrt[1 - z] (145536 - 816320 z + 3882480 z^2 - 6044520 z^3 + 38289170 z^4 - 89699301 z^5 + 127573245 z^6 - 113089305 z^7 + 61553205 z^8 - 18905850 z^9 + 2517060 z^10) Log[1 - E^(I ArcSin[Sqrt[z]])]) + (1/(24576 (-1 + z)^8)) (Sqrt[1 - z] (145536 - 816320 z + 3882480 z^2 - 6044520 z^3 + 38289170 z^4 - 89699301 z^5 + 127573245 z^6 - 113089305 z^7 + 61553205 z^8 - 18905850 z^9 + 2517060 z^10) Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))]) - (3675/512) z^(5/2) ArcSin[Sqrt[z]] Log[(1 - E^(I ArcSin[Sqrt[z]]))/ (1 + E^(I ArcSin[Sqrt[z]]))] + (1/(24576 (-1 + z)^8)) (Sqrt[1 - z] (145536 - 816320 z + 3882480 z^2 - 6044520 z^3 + 38289170 z^4 - 89699301 z^5 + 127573245 z^6 - 113089305 z^7 + 61553205 z^8 - 18905850 z^9 + 2517060 z^10) Log[1 + E^(I ArcSin[Sqrt[z]])]) - (3675/512) I z^(5/2) PolyLog[2, -E^(I ArcSin[Sqrt[z]])] + (3675/512) I z^(5/2) PolyLog[2, E^(I ArcSin[Sqrt[z]])]

Standard Form

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MathML Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]