Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.aa8j)

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=4

For fixed z and a₁=-5/2, a₂=-1/2, a₃=4, b₁=1/2

http://functions.wolfram.com/07.27.03.aa8j.01

Input Form

HypergeometricPFQ[{-(5/2), -(1/2), 4}, {1/2, 7/2}, z] == (-30 - 235 z + 44571 z^2 + 43785 z^3 - 10395 z^4)/(49152 z^2) - (5 (2 + 15 z + 300 z^2 + 2140 z^3 - 3150 z^4 + 693 z^5) Log[1 - Sqrt[z]])/ (32768 z^(5/2)) + (5 (2 + 15 z + 300 z^2 + 2140 z^3 - 3150 z^4 + 693 z^5) 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]