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

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=3, a₃>=3

For fixed z and a₁=3, a₂=3, a₃=7/2

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

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

Input Form

HypergeometricPFQ[{3, 3, 7/2}, {-(7/2), 1/2}, z] == (1/(2240 (-1 + z)^12)) (2240 - 67200 z + 1018752 z^2 - 12529664 z^3 + 250443072 z^4 + 2127795120 z^5 + 3217421320 z^6 + 1311833634 z^7 + 129980757 z^8 + 1527374 z^9) + (1287 (16016 z^(9/2) + 61880 z^(11/2) + 59990 z^(13/2) + 16955 z^(15/2) + 1160 z^(17/2) + 8 z^(19/2)) ArcSin[Sqrt[z]])/ (64 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]