Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.5384)

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=3

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

http://functions.wolfram.com/07.27.03.5384.01

Input Form

HypergeometricPFQ[{-(7/2), -(1/2), 3}, {1/2, 7/2}, z] == (-105 - 350 z + 44301 z^2 + 49203 z^3 - 18690 z^4 + 3465 z^5)/(49152 z^2) + (35 (-1 - 3 z - 45 z^2 - 320 z^3 + 525 z^4 - 189 z^5 + 33 z^6) Log[1 - Sqrt[z]])/(32768 z^(5/2)) - (35 (-1 - 3 z - 45 z^2 - 320 z^3 + 525 z^4 - 189 z^5 + 33 z^6) Log[1 + Sqrt[z]])/(32768 z^(5/2)) - (2625 Sqrt[z] PolyLog[2, -Sqrt[z]])/ 4096 + (2625 Sqrt[z] PolyLog[2, Sqrt[z]])/4096

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]