Meijer G-function: Specific values (formula 07.34.03.1015)

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/07.34.03.1015.01

Input Form

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