Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.avb3)

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=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=4, a₃>=4

For fixed z and a₁=7/2, a₂=4, a₃=4

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

http://functions.wolfram.com/07.27.03.avb3.01

Input Form

HypergeometricPFQ[{7/2, 4, 4}, {-(7/2), 1/2}, -z] == (1/(256 (1 + z)^14)) (256 + 11776 z + 260864 z^2 + 4721664 z^3 + 143100160 z^4 - 2055305616 z^5 + 5797859704 z^6 - 5270785574 z^7 + 1640847547 z^8 - 152737288 z^9 + 2605156 z^10) - (45045 (11440 z^(9/2) - 74568 z^(11/2) + 137090 z^(13/2) - 89253 z^(15/2) + 20538 z^(17/2) - 1400 z^(19/2) + 16 z^(21/2)) ArcSinh[Sqrt[z]])/ (256 Sqrt[1 + z] (1 + 14 z + 91 z^2 + 364 z^3 + 1001 z^4 + 2002 z^5 + 3003 z^6 + 3432 z^7 + 3003 z^8 + 2002 z^9 + 1001 z^10 + 364 z^11 + 91 z^12 + 14 z^13 + z^14))

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]