Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.and7)

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=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=4

For fixed z and a₁=1/2, a₂=1, a₃=4, b₁=-7/2

http://functions.wolfram.com/07.27.03.and7.01

Input Form

HypergeometricPFQ[{1/2, 1, 4}, {-(7/2), -(7/2)}, -z] == (1/(3920 (1 + z)^12)) (3920 + 46400 z + 251808 z^2 + 824256 z^3 + 2290608 z^4 - 57847680 z^5 + 581202880 z^6 - 1152798944 z^7 + 531151632 z^8 - 18914049 z^9 - 1168650 z^10 - 52920 z^11) - (1287 (128 z^(9/2) - 3840 z^(11/2) + 18720 z^(13/2) - 22880 z^(15/2) + 6435 z^(17/2)) ArcSinh[Sqrt[z]])/(112 Sqrt[1 + z] (1 + 12 z + 66 z^2 + 220 z^3 + 495 z^4 + 792 z^5 + 924 z^6 + 792 z^7 + 495 z^8 + 220 z^9 + 66 z^10 + 12 z^11 + z^12))

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]