Meijer G-function: Specific values (formula 07.34.03.0973)

MeijerG

$Mathematica Notation$

Hypergeometric Functions

MeijerG[{{a₁,...,a_n},{a_n+1,...,a_p}},{{b₁,...,b_m},{b_m+1,...,b_q}},z]

Specific values

Specialized values

Cases with m==3

Case {m,n,p,q}={3,0,2,6}

http://functions.wolfram.com/07.34.03.0973.01

Input Form

MeijerG[{{}, {Subscript[a, 1], Subscript[a, 2]}}, {{Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, {Subscript[b, 4], Subscript[b, 5], Subscript[b, 6]}}, z] == ((Pi^2 Csc[Pi (-Subscript[b, 1] + Subscript[b, 2])] Csc[Pi (-Subscript[b, 1] + Subscript[b, 3])])/ (Gamma[Subscript[a, 1] - Subscript[b, 1]] Gamma[Subscript[a, 2] - Subscript[b, 1]])) z^Subscript[b, 1] HypergeometricPFQRegularized[{1 - Subscript[a, 1] + Subscript[b, 1], 1 - Subscript[a, 2] + Subscript[b, 1]}, {1 + Subscript[b, 1] - Subscript[b, 2], 1 + Subscript[b, 1] - Subscript[b, 3], 1 + Subscript[b, 1] - Subscript[b, 4], 1 + Subscript[b, 1] - Subscript[b, 5], 1 + Subscript[b, 1] - Subscript[b, 6]}, -z] + ((Pi^2 Csc[Pi (Subscript[b, 1] - Subscript[b, 2])] Csc[Pi (-Subscript[b, 2] + Subscript[b, 3])])/ (Gamma[Subscript[a, 1] - Subscript[b, 2]] Gamma[Subscript[a, 2] - Subscript[b, 2]])) z^Subscript[b, 2] HypergeometricPFQRegularized[{1 - Subscript[a, 1] + Subscript[b, 2], 1 - Subscript[a, 2] + Subscript[b, 2]}, {1 - Subscript[b, 1] + Subscript[b, 2], 1 + Subscript[b, 2] - Subscript[b, 3], 1 + Subscript[b, 2] - Subscript[b, 4], 1 + Subscript[b, 2] - Subscript[b, 5], 1 + Subscript[b, 2] - Subscript[b, 6]}, -z] + ((Pi^2 Csc[Pi (Subscript[b, 1] - Subscript[b, 3])] Csc[Pi (Subscript[b, 2] - Subscript[b, 3])])/ (Gamma[Subscript[a, 1] - Subscript[b, 3]] Gamma[Subscript[a, 2] - Subscript[b, 3]])) z^Subscript[b, 3] HypergeometricPFQRegularized[{1 - Subscript[a, 1] + Subscript[b, 3], 1 - Subscript[a, 2] + Subscript[b, 3]}, {1 - Subscript[b, 1] + Subscript[b, 3], 1 - Subscript[b, 2] + Subscript[b, 3], 1 + Subscript[b, 3] - Subscript[b, 4], 1 + Subscript[b, 3] - Subscript[b, 5], 1 + Subscript[b, 3] - Subscript[b, 6]}, -z] /; !Element[Subscript[b, 2] - Subscript[b, 1], Integers] && !Element[Subscript[b, 3] - Subscript[b, 1], Integers] && !Element[Subscript[b, 3] - Subscript[b, 2], Integers]

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

MeijerG[{{a₁,...,a_n},{a_n+1,...,a_p}},{{b₁,...,b_m},{b_m+1,...,b_q}},z,r]