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Published: 30/07/2016Fractional integrals are easier to define than fractional derivatives. And for sufficiently smooth functions, you can use the former to define the latter. The RiemannLiouville fractional integral sta ... Read moreSource: www.johndcook.com


Published: 28/07/2016Eberhard Zwicker proposed a model for combining several psychoacoustic metrics into one metric to quantify annoyance. It is a function of three things: N5, the 95th percentile of loudness, measured in ... Read moreSource: www.johndcook.com

Published: 26/07/2016There are many ways to define fractional derivatives, and in general they coincide on nice classes of functions. A long time ago I wrote about one way to define fractional derivatives using Fourier tr ... Read moreSource: www.johndcook.com

Published: 19/07/2016There are four basic types of integral equations. There are many other integral equations, but if you are familiar with these four, you have a good overview of the classical theory. All four involve t ... Read moreSource: www.johndcook.com

Published: 17/07/2016The MittagLeffler function is a generalization of the exponential function. Since k!= Γ(k + 1), we can write the exponential function’s power series as and we can generalize this to the Mittag= ... Read moreSource: www.johndcook.com

Published: 14/07/2016A few weeks ago I started a series of posts on various things you could do with a functional fold. In the first post I mentioned that the idea came from a paper by Brian Beckman on Kalman filters and ... Read moreSource: www.johndcook.com

Published: 11/07/2016I heard someone say the other day that the advantage of formal software validation methods is that they let you explore the corners, cases where intuition doesn’t naturally take you. This made m ... Read moreSource: www.johndcook.com

Published: 10/07/2016The best way to develop software doesn’t exist. There’s only the best way that you know of, for a particular problem, with particular people, given their skills, experience, and constraint ... Read moreSource: www.johndcook.com

Published: 5/07/2016This post explores a sentence from the book Single Digits: Any number in Pascal’s triangle that is not in the outer two layers will appear at least three times, usually four. Pascal’s tria ... Read moreSource: www.johndcook.com

Published: 4/07/2016One of the things I learned from my tenure as a software project manager was that a project is more likely to succeed if there’s a way to get where you want to go continuously. You want to move ... Read moreSource: www.johndcook.com
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