Meijer G-function: Specific values (formula 07.34.03.1068)

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==4

Case {m,n,p,q}={4,1,4,4}

http://functions.wolfram.com/07.34.03.1068.01

Input Form

MeijerG[{{a}, {c, d, a - c + d}}, {{b, -1 + a - b + d, (1/2) (-1 + a + d), (a + d)/2}, {}}, z] == ((2^(a - d) Sqrt[Pi] Gamma[1 - a + b] Gamma[-b + d])/ (Gamma[1 - a + c] Gamma[1 - c + d])) z^(-1 + a) Hypergeometric2F1[1 - a + b, -b + d, 1 - a + c, (1/(2 Sqrt[z])) (Sqrt[z] - Sqrt[1 + z])] Hypergeometric2F1[1 - a + b, -b + d, 1 - c + d, (1/(2 Sqrt[z])) (Sqrt[z] - Sqrt[1 + z])] /; !IntervalMemberQ[Interval[{-Infinity, 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]