Meijer G-function: Specific values (formula 07.34.03.1009)

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/07.34.03.1009.01

Input Form

MeijerG[{{a}, {c, 2 c - a - 1}}, {{b, -1 - b + 2 c, -(1/2) + c}, {}}, z] == (-((2^(1 + 2 a - 2 c) (a - c) Sqrt[Pi] Gamma[1 - a + b] Gamma[-a - b + 2 c])/ Gamma[1 - a + c]^2)) z^(-1 + a) Hypergeometric2F1[(1/2) (1 - a + b), (1/2) (-a - b + 2 c), -a + c, -(1/z)] Hypergeometric2F1[(1/2) (1 - a + b), (1/2) (-a - b + 2 c), 1 - a + c, -(1/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]