Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.0144)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]

Specific values

Specialized values

For fixed z and with symbolical integers in parameters

http://functions.wolfram.com/07.27.03.0144.01

Input Form

HypergeometricPFQ[{m/p, n/q, 1}, {m/p + 1, n/q + 1}, z] == ((m n)/(n p - m q)) (Sum[Exp[-((2 Pi I k n)/q)] Log[1 - z^(1/q) Exp[(2 Pi I k)/q]], {k, 0, q - 1}]/z^(n/q) - Sum[Exp[-((2 Pi I k m)/p)] Log[1 - z^(1/p) Exp[(2 Pi I k)/p]], {k, 0, p - 1}]/z^(m/p) + q Sum[1/(z^k (n - k q)), {k, 1, -1 - Floor[-(n/q)]}]) /; Element[m, Integers] && m > 0 && Element[n, Integers] && n > 0 && Element[p, Integers] && p > 0 && Element[q, Integers] && Inequality[q, Greater, 0 n p, Unequal, m q] && m <= p

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)

2001-10-29

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]