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

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=4

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

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

Input Form

HypergeometricPFQ[{3, 3, 4}, {-(7/2), 1}, z] == (1/(7168 (-1 + z)^12)) (7168 - 159744 z + 1947648 z^2 - 20074496 z^3 + 343778304 z^4 + 2471050923 z^5 + 3132701986 z^6 + 1026208656 z^7 + 71772768 z^8 + 192192 z^9) + (6435 (20449 z^(9/2) + 67600 z^(11/2) + 55000 z^(13/2) + 12384 z^(15/2) + 576 z^(17/2)) ArcSin[Sqrt[z]])/(1024 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]