Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.5629)

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=4

For fixed z and a₁=-7/2, a₂=-1/2, a₃=4, b₁=1/2

http://functions.wolfram.com/07.27.03.5629.01

Input Form

HypergeometricPFQ[{-(7/2), -(1/2), 4}, {1/2, 7/2}, z] == (-105 - 980 z + 270951 z^2 + 432369 z^3 - 203280 z^4 + 45045 z^5)/ (294912 z^2) + (35 (-1 - 9 z - 225 z^2 - 2840 z^3 + 4725 z^4 - 2079 z^5 + 429 z^6) Log[1 - Sqrt[z]])/(196608 z^(5/2)) - (35 (-1 - 9 z - 225 z^2 - 2840 z^3 + 4725 z^4 - 2079 z^5 + 429 z^6) Log[1 + Sqrt[z]])/(196608 z^(5/2)) - (6125 Sqrt[z] PolyLog[2, -Sqrt[z]])/ 8192 + (6125 Sqrt[z] PolyLog[2, Sqrt[z]])/8192

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]