Representation of Other Functions in Terms of The G-function
The following list shows how the familiar elementary functions result as special cases of the Meijer G-function:
Here, H denotes the Heaviside step function.
The subsequent list shows how some higher functions can be expressed in terms of the G-function:
Even the derivatives of γ(α,x) and Γ(α,x) with respect to α can be expressed in terms of the Meijer G-function. Here, γ and Γ are the lower and upper incomplete gamma functions, Jν and Yν are the Bessel functions of the first and second kind, respectively, Iν and Kν are the corresponding modified Bessel functions, and Φ is the Lerch transcendent.
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