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:

    “Painting myself for others, I have painted my inward self with colors clearer than my original ones. I have no more made my book than my book has made me—a book consubstantial with its author, concerned with my own self, an integral part of my life; not concerned with some third-hand, extraneous purpose, like all other books.”
    —Michel de Montaigne (1533–1592)

    “Now, since our condition accommodates things to itself, and transforms them according to itself, we no longer know things in their reality; for nothing comes to us that is not altered and falsified by our Senses. When the compass, the square, and the rule are untrue, all the calculations drawn from them, all the buildings erected by their measure, are of necessity also defective and out of plumb. The uncertainty of our senses renders uncertain everything that they produce.”
    —Michel de Montaigne (1533–1592)

    “I have no acting technique.... I act instinctively. That’s why I can’t play any role that isn’t based on something in my life.”
    —Ethel Waters (1900–1977)