Regularized generalized hypergeometric function: Series representations (formula 07.32.06.0034)

HypergeometricPFQRegularized

$Mathematica Notation$

Hypergeometric Functions

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

Series representations

Asymptotic series expansions

Expansions for ₀F₂

http://functions.wolfram.com/07.32.06.0034.01

Input Form

HypergeometricPFQRegularized[{}, {Subscript[b, 1], Subscript[b, 2]}, z] \[Proportional] (1/(2 Sqrt[3] Pi)) E^(3 z^(1/3)) z^((1/3) (1 - Subscript[b, 1] - Subscript[b, 2])) (1 + (-2 - 3 Subscript[b, 1]^2 + 3 Subscript[b, 2] - 3 Subscript[b, 2]^2 + 3 Subscript[b, 1] (1 + Subscript[b, 2]))/(9 z^(1/3)) + (1/(162 z^(2/3))) (4 + 9 Subscript[b, 1]^4 - 12 Subscript[b, 2] + 3 Subscript[b, 2]^2 - 12 Subscript[b, 2]^3 + 9 Subscript[b, 2]^4 - 6 Subscript[b, 1]^3 (2 + 3 Subscript[b, 2]) + 3 Subscript[b, 1]^2 (1 - 3 Subscript[b, 2] + 9 Subscript[b, 2]^2) - 3 Subscript[b, 1] (4 - 17 Subscript[b, 2] + 3 Subscript[b, 2]^2 + 6 Subscript[b, 2]^3)) + \[Ellipsis]) /; (Abs[z] -> Infinity)

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]