Meijer G-function: Specific values (formula 07.34.03.0547)

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==1

Case {m,n,p,q}={1,3,3,3}

http://functions.wolfram.com/07.34.03.0547.01

Input Form

MeijerG[{{a, c, 2 a - c}, {}}, {{b}, {-(1/2) + a, 2 a - b}}, z] == ((Sqrt[Pi] Gamma[1 + b - c] Gamma[1 - 2 a + b + c])/Sqrt[1 + z]) z^a LegendreP[-(1/2) - a + c, -(1/2) + a - b, 3, Sqrt[1 + z]] LegendreP[-(1/2) - a + c, 1/2 + a - b, 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]