Meijer G-function - Integral Transforms Based On The G-function

Integral Transforms Based On The G-function

In general, two functions k(z,y) and h(z,y) are called a pair of transform kernels if, for any suitable function f(z) or any suitable function g(z), the following two relationships hold simultaneously:


g(z) = \int_{0}^{\infty} k(z,y) \, f(y) \; dy, \quad
f(z) = \int_{0}^{\infty} h(z,y) \, g(y) \; dy.

The pair of kernels is said to be symmetric if k(z,y) = h(z,y).

Read more about this topic:  Meijer G-function

Famous quotes containing the words integral, transforms and/or based:

    Make the most of your regrets; never smother your sorrow, but tend and cherish it till it come to have a separate and integral interest. To regret deeply is to live afresh.
    Henry David Thoreau (1817–1862)

    It is old age, rather than death, that is to be contrasted with life. Old age is life’s parody, whereas death transforms life into a destiny: in a way it preserves it by giving it the absolute dimension. ... Death does away with time.
    Simone De Beauvoir (1908–1986)

    The trouble with this country is that there are too many politicians who believe, with a conviction based on experience, that you can fool all of the people all of the time.
    Franklin Pierce Adams (1881–1960)