g-function | Meijer function

The Meijer G-function is a very general function which reduces to simpler special functions in many common cases. The Meijer G-function is defined by G_(p, q)^(m, n)(x|a_1, ..., a_p b_1, ..., b_q) congruent 1/(2π i) integral_(γ_L) ( product_(j = 1)^m Γ(b_j - s) product_(j = 1)^n Γ(1 - a_j + s))/( product_(j = n + 1)^p Γ(a_j - s) product_(j = m + 1)^q Γ(1 - b_j + s)) x^s d s, where Γ(s) is the gamma function . A different but equivalent form is used by Prudnikov et al. (1990, p. 793), G_(p, q)^(m, n)(x|a_1, ..., a_p b_1, ..., b_q) congruent 1/(2π i) integral_(γ_L) ( product_(j = 1)^m Γ(b_j + s) product_(j = 1)^n Γ(1 - a_j - s))/( product_(j = n + 1)^p Γ(a_j + s) product_(j = m + 1)^q Γ(1 - b_j - s)) x^(-s) d s, This form provides more consistency with the definition of this function via an inverse Mellin transform.

Barnes G-function | Fox H-function | G-transform | Kampé de Fériet function | MacRobert's E-function | Ramanujan g- and G-functions