Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.2722)

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=-5/2, a₃>=-5/2

For fixed z and a₁=-7/2, a₂=-5/2, a₃=1

For fixed z and a₁=-7/2, a₂=-5/2, a₃=1, b₁=1/2

http://functions.wolfram.com/07.27.03.2722.01

Input Form

HypergeometricPFQ[{-(7/2), -(5/2), 1}, {1/2, 5/2}, z] == (105 + 14319 z + 65709 z^2 + 29015 z^3 + 420 z^4)/(16384 z) + (105 (1 - 20 z - 220 z^2 + 80 z^3 + 155 z^4 + 4 z^5) Log[1 - Sqrt[z]])/ (32768 z^(3/2)) - (105 (1 - 20 z - 220 z^2 + 80 z^3 + 155 z^4 + 4 z^5) Log[1 + Sqrt[z]])/(32768 z^(3/2)) - (1575 Sqrt[z] (2 + 4 z + z^2) PolyLog[2, -Sqrt[z]])/4096 + (1575 Sqrt[z] (2 + 4 z + z^2) 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]