Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.4330)

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=-3/2, a₃>=-3/2

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

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

http://functions.wolfram.com/07.27.03.4330.01

Input Form

HypergeometricPFQ[{-(7/2), -(3/2), 3}, {-(1/2), 5/2}, z] == (3 (-70 + 12055 z - 141071 z^2 - 62685 z^3 + 10395 z^4))/(40960 z) + (21 (-2 - 45 z + 900 z^2 + 740 z^3 - 1890 z^4 + 297 z^5) Log[1 - Sqrt[z]])/ (16384 z^(3/2)) - (21 (-2 - 45 z + 900 z^2 + 740 z^3 - 1890 z^4 + 297 z^5) Log[1 + Sqrt[z]])/(16384 z^(3/2)) + (11025 z^(3/2) PolyLog[2, -Sqrt[z]])/ 2048 - (11025 z^(3/2) PolyLog[2, Sqrt[z]])/2048

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]