Meijer G-function: Specific values (formula 07.34.03.0595)

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}={1,4,4,4}

http://functions.wolfram.com/07.34.03.0595.01

Input Form

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

Standard Form

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MathML Form

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</mo> <mrow> <mi> z </mi> <mo> ∉ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> ∞ </mi> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>

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]