Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.1961)

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=3

For fixed z and a₁=-7/2, a₂=-7/2, a₃=3, b₁=-1/2

http://functions.wolfram.com/07.27.03.1961.01

Input Form

HypergeometricPFQ[{-(7/2), -(7/2), 3}, {-(1/2), 5/2}, z] == -((3 (490 - 199915 z + 5693751 z^2 + 25813445 z^3 + 7828485 z^4))/ (655360 z)) - (147 (2 + 75 z - 3000 z^2 - 38900 z^3 + 21750 z^4 + 20073 z^5) Log[1 - Sqrt[z]])/(262144 z^(3/2)) + (147 (2 + 75 z - 3000 z^2 - 38900 z^3 + 21750 z^4 + 20073 z^5) Log[1 + Sqrt[z]])/(262144 z^(3/2)) + (2205 z^(3/2) (350 + 630 z + 99 z^2) PolyLog[2, -Sqrt[z]])/32768 - (2205 z^(3/2) (350 + 630 z + 99 z^2) PolyLog[2, Sqrt[z]])/32768

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]