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

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=-3/2, a₂>=-3/2

For fixed z and a₁=-3/2, a₂=1, a₃>=1

For fixed z and a₁=-3/2, a₂=1, a₃=3

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

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

Input Form

HypergeometricPFQ[{-(3/2), 1, 3}, {3/2, 5/2}, -z] == (-96 + 216 Pi^2 Sqrt[z] + 1880 z + 540 Pi^2 z^(3/2) + 1260 z^2 + 315 Pi^2 z^(5/2))/(4096 z) + ((312 + 412 z - 129 z^2 - 652 z^3 - 471 z^4 - 108 z^5) Log[1 + Sqrt[z] - Sqrt[1 + z]])/(1024 (1 + z)^(7/2)) + ((-312 - 412 z + 129 z^2 + 652 z^3 + 471 z^4 + 108 z^5) Log[1 - Sqrt[z] + Sqrt[1 + z]])/(1024 (1 + z)^(7/2)) + (3 Sqrt[1 + z] (8 + 110 z + 105 z^2) Log[Sqrt[z] + Sqrt[1 + z]])/ (1024 z^(3/2)) + ((-312 - 412 z + 129 z^2 + 652 z^3 + 471 z^4 + 108 z^5) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/ (1024 (1 + z)^(7/2)) + (9 (24 + 60 z + 35 z^2) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/ (1024 Sqrt[z]) + (9 (24 + 60 z + 35 z^2) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/(1024 Sqrt[z]) - (9 (24 + 60 z + 35 z^2) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/ (1024 Sqrt[z])

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]