Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.aa1t)

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=-5/2, a₂>=-5/2

For fixed z and a₁=-5/2, a₂=-1/2, a₃>=-1/2

For fixed z and a₁=-5/2, a₂=-1/2, a₃=3

For fixed z and a₁=-5/2, a₂=-1/2, a₃=3, b₁=1/2

http://functions.wolfram.com/07.27.03.aa1t.01

Input Form

HypergeometricPFQ[{-(5/2), -(1/2), 3}, {1/2, 7/2}, z] == (-30 - 85 z + 7261 z^2 + 4935 z^3 - 945 z^4)/(8192 z^2) - (15 (2 + 5 z + 60 z^2 + 220 z^3 - 350 z^4 + 63 z^5) Log[1 - Sqrt[z]])/ (16384 z^(5/2)) + (15 (2 + 5 z + 60 z^2 + 220 z^3 - 350 z^4 + 63 z^5) Log[1 + Sqrt[z]])/(16384 z^(5/2)) - (1125 Sqrt[z] PolyLog[2, -Sqrt[z]])/ 2048 + (1125 Sqrt[z] 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]