Meijer G-function: Specific values (formula 07.34.03.1022)

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}={3,1,3,3}

http://functions.wolfram.com/07.34.03.1022.01

Input Form

MeijerG[{{a}, {c, -a + 2 c}}, {{b, -1 - b + 2 c, c - 1/2}, {}}, z] == (-((2 E^(2 I (b - c) Pi) Gamma[1 - a + b])/(Sqrt[Pi] Gamma[-a - b + 2 c]))) z^(-(1/2) + c) LegendreQ[-(1/2) - a + c, -(1/2) - b + c, 3, Sqrt[1 + z]]^ 2 /; !IntervalMemberQ[Interval[{-1, 0}], z]

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]