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.
Read more about this topic: Meijer G-function
Famous quotes containing the words representation of, functions and/or terms:
“America loves the representation of its heroes to be not just larger than life, but stupendously, awesomely bigger than anything else. If blue whales built statues to each other they’d be smaller then these.”
—Simon Hoggart (b. 1946)
“Those things which now most engage the attention of men, as politics and the daily routine, are, it is true, vital functions of human society, but should be unconsciously performed, like the corresponding functions of the physical body.”
—Henry David Thoreau (1817–1862)
“I am happy to find you are on good terms with your neighbors. It is almost the most important circumstance in life, since nothing is so corroding as frequently to meet persons with whom one has any difference.”
—Thomas Jefferson (1743–1826)