Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.2253)

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=-7/2, a₃>=-7/2

For fixed z and a₁=-7/2, a₂=-7/2, a₃=4

For fixed z and a₁=-7/2, a₂=-7/2, a₃=4, b₁=3/2

http://functions.wolfram.com/07.27.03.2253.01

Input Form

HypergeometricPFQ[{-(7/2), -(7/2), 4}, {3/2, 3/2}, z] == (8419209 + 143255371 z + 256089925 z^2 + 53055975 z^3)/9437184 + (1225 (-217 - 10144 z - 20592 z^2 + 21664 z^3 + 9289 z^4) Log[1 - Sqrt[z]])/ (6291456 Sqrt[z]) - (1225 (-217 - 10144 z - 20592 z^2 + 21664 z^3 + 9289 z^4) Log[1 + Sqrt[z]])/(6291456 Sqrt[z]) - (1225 (5 + 560 z + 3780 z^2 + 3696 z^3 + 429 z^4) PolyLog[2, -Sqrt[z]])/ (524288 Sqrt[z]) + (1225 (5 + 560 z + 3780 z^2 + 3696 z^3 + 429 z^4) PolyLog[2, Sqrt[z]])/(524288 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]