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

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, a₂>=1

For fixed z and a₁=1, a₂=3/2, a₃>=3/2

For fixed z and a₁=1, a₂=3/2, a₃=3

For fixed z and a₁=1, a₂=3/2, a₃=3, b₁=-7/2

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

Input Form

HypergeometricPFQ[{1, 3/2, 3}, {-(7/2), -(7/2)}, -z] == (1/(1960 (1 + z)^12)) (1960 + 22800 z + 121872 z^2 + 388544 z^3 + 1747992 z^4 - 125021040 z^5 + 1337052640 z^6 - 3175089984 z^7 + 2068815672 z^8 - 317147754 z^9 + 2877525 z^10 + 39690 z^11) + (1287 (-256 z^(9/2) + 8320 z^(11/2) - 45760 z^(13/2) + 68640 z^(15/2) - 30030 z^(17/2) + 3003 z^(19/2)) ArcSinh[Sqrt[z]])/ (56 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]