Regularized generalized hypergeometric function: Specific values (formula 07.32.03.0039)

HypergeometricPFQRegularized

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQRegularized[{a₁,...,a_p},{b₁,...,b_q},z]

Specific values

Specialized values

Case _q+1F^~_qat z==1

http://functions.wolfram.com/07.32.03.0039.01

Input Form

HypergeometricPFQRegularized[{-n, a/(q + 1), (a + 1)/(q + 1), \[Ellipsis], (a + q)/(q + 1), b/q, (b + 1)/q, \[Ellipsis], (b + q - 1)/q}, {(a + 1)/q, (a + 2)/q, \[Ellipsis], (a + q)/q, (b - n)/(q + 1), (b - n + 1)/(q + 1), \[Ellipsis], (b - n + q)/(q + 1)}, 1] == ((-1)^n (2 Pi)^(1/2 - q) q^(1/2 + a) (1 + q)^(b - n - 1/2) Pochhammer[1 + a - b, n])/(Gamma[1 + a] Gamma[b]) /; Element[n, Integers] && n > 0

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

HypergeometricPFQRegularized[{},{b},z]
HypergeometricPFQRegularized[{a₁},{b₁},z]
HypergeometricPFQRegularized[{a₁,a₂},{b₁},z]