Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.6104)

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=1/2, a₃>=1/2

For fixed z and a₁=-7/2, a₂=1/2, a₃=2

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

http://functions.wolfram.com/07.27.03.6104.01

Input Form

HypergeometricPFQ[{-(7/2), 1/2, 2}, {3/2, 7/2}, z] == (-630 + 2310 z + 20991 z^2 - 13979 z^3 + 5565 z^4 - 945 z^5)/(49152 z^2) - (35 (6 - 24 z + 155 z^2 - 240 z^3 + 150 z^4 - 56 z^5 + 9 z^6) Log[1 - Sqrt[z]])/(32768 z^(5/2)) + (35 (6 - 24 z + 155 z^2 - 240 z^3 + 150 z^4 - 56 z^5 + 9 z^6) Log[1 + Sqrt[z]])/(32768 z^(5/2)) - (525 PolyLog[2, -Sqrt[z]])/ (4096 Sqrt[z]) + (525 PolyLog[2, Sqrt[z]])/(4096 Sqrt[z])

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]