Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.av17)

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, a₂>=3

For fixed z and a₁=3, a₂=7/2, a₃>=7/2

For fixed z and a₁=3, a₂=7/2, a₃=4

For fixed z and a₁=3, a₂=7/2, a₃=4, b₁=-3/2

http://functions.wolfram.com/07.27.03.av17.01

Input Form

HypergeometricPFQ[{3, 7/2, 4}, {-(3/2), -(3/2)}, -z] == (1/(384 (1 + z)^13)) (384 - 2176 z + 1227008 z^2 - 248901120 z^3 + 4116415232 z^4 - 17158195648 z^5 + 23716848672 z^6 - 11489848986 z^7 + 1770119295 z^8 - 60266934 z^9 + 52920 z^10) + (1155 (-5376 z^(5/2) + 256896 z^(7/2) - 2251968 z^(9/2) + 6091360 z^(11/2) - 5944950 z^(13/2) + 2107413 z^(15/2) - 237468 z^(17/2) + 5544 z^(19/2)) ArcSinh[Sqrt[z]])/ (128 Sqrt[1 + z] (1 + 13 z + 78 z^2 + 286 z^3 + 715 z^4 + 1287 z^5 + 1716 z^6 + 1716 z^7 + 1287 z^8 + 715 z^9 + 286 z^10 + 78 z^11 + 13 z^12 + z^13))

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

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]