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

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=3, a₃>=3

For fixed z and a₁=3/2, a₂=3, a₃=3

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

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

Input Form

HypergeometricPFQ[{3/2, 3, 3}, {-(5/2), -(5/2)}, -z] == (1/(1600 (1 + z)^12)) (1600 + 15744 z + 94848 z^2 - 3091456 z^3 + 495750720 z^4 - 5630044800 z^5 + 14891503264 z^6 - 11519098272 z^7 + 2495966319 z^8 - 101591490 z^9) + (693 (12672 z^(7/2) - 436480 z^(9/2) + 2600800 z^(11/2) - 4391200 z^(13/2) + 2337225 z^(15/2) - 352968 z^(17/2) + 9240 z^(19/2)) ArcSinh[Sqrt[z]])/(320 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]