Meijer G-function: Specific values (formula 07.34.03.1000)

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/07.34.03.1000.01

Input Form

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