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:

    “An island always pleases my imagination, even the smallest, as a small continent and integral portion of the globe. I have a fancy for building my hut on one. Even a bare, grassy isle, which I can see entirely over at a glance, has some undefined and mysterious charm for me.”
    —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)

    “Because it is not always easy for an adult to predict what inaccurate ideas a child may have, it can help to answer questions first with one of your own: “What do you think?” Once you find out what a child is really asking, you’ll be in a better position to give a helpful answer based on the facts.”
    —Joanna Cole (20th century)