Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ah66)

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=-3/2, a₂>=-3/2

For fixed z and a₁=-3/2, a₂=2, a₃>=2

For fixed z and a₁=-3/2, a₂=2, a₃=2

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

http://functions.wolfram.com/07.27.03.ah66.01

Input Form

HypergeometricPFQ[{-(3/2), 2, 2}, {3/2, 7/2}, z] == (5 I (-576 I + 288 I z + 144 Pi^2 z^(3/2) - 1528 I z^2 - 432 Pi^2 z^(5/2) + 900 I z^3 + 225 Pi^2 z^(7/2)))/(16384 z^2) - (15 Sqrt[1 - z] (48 - 8 z - 94 z^2 + 75 z^3) ArcSin[Sqrt[z]])/ (4096 z^(5/2)) + (1/(4096 (-1 + z)^5)) (5 Sqrt[1 - z] (-4880 - 30240 z + 67023 z^2 - 87589 z^3 + 63609 z^4 - 24363 z^5 + 3840 z^6) Log[1 - E^(I ArcSin[Sqrt[z]])]) - (1/(4096 (-1 + z)^5)) (5 Sqrt[1 - z] (-4880 - 30240 z + 67023 z^2 - 87589 z^3 + 63609 z^4 - 24363 z^5 + 3840 z^6) Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))]) + (45 (16 - 48 z + 25 z^2) ArcSin[Sqrt[z]] Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))])/ (4096 Sqrt[z]) - (1/(4096 (-1 + z)^5)) (5 Sqrt[1 - z] (-4880 - 30240 z + 67023 z^2 - 87589 z^3 + 63609 z^4 - 24363 z^5 + 3840 z^6) Log[1 + E^(I ArcSin[Sqrt[z]])]) + (45 I (16 - 48 z + 25 z^2) PolyLog[2, -E^(I ArcSin[Sqrt[z]])])/ (4096 Sqrt[z]) - (45 I (16 - 48 z + 25 z^2) PolyLog[2, E^(I ArcSin[Sqrt[z]])])/(4096 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]