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)

    “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)

    “Justice in the hands of the powerful is merely a governing system like any other. Why call it justice? Let us rather call it injustice, but of a sly effective order, based entirely on cruel knowledge of the resistance of the weak, their capacity for pain, humiliation and misery. Injustice sustained at the exact degree of necessary tension to turn the cogs of the huge machine-for- the-making-of-rich-men, without bursting the boiler.”
    —Georges Bernanos (1888–1948)