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#DifferenceTransform

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“A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs; it is because they are made with ideas.”
― G.H. Hardy, A Mathematician's Apology

Let's define something...
Difference transform
D{f}(a,b):=ab(f(x)f(x)) dx

Here an operator D is acting on a function f, describing the difference between an indiscrete sum and a discrete sum on a certain interval a to b. This operator may play a pivotal role in asymptotic expansions, analytic continuation, etc.