Meijer G-function: Specific values (formula 07.34.03.0739)

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==2

Case {m,n,p,q}={2,1,2,2}

http://functions.wolfram.com/07.34.03.0739.01

Input Form

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