In this new version of Reference for Functional Equations I added several more z-transform pairs. I also started to add binomial transform pairs. The definition for the binomial is not consistent among different authors. I arbitrarily chose one, and later I changed it. I will probably change it again. Several typos were fixed. I am working on a system to include proofs so that the tables can be checked more easily.
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I have not posted in a while; one reason is that I got sucked into some interesting mathematics; the work-in-progress Reference for Functional Equations is the result. If you are interested in such things – have a look.
Original image by openDemocracy.
The document below contains tables and formulas useful for working with functional equations, especially di fference equations, and to a lesser extent, quotient equations (where differences are replaced by quotients).
The reference contains tables for differences, sums, quotients, and products. There is also a table of z-transforms, binomial transofroms, formulas for converting certain kinds of functional equations to difference equations and some discrete Taylor series. There are more than 300 formulas in its 30 pages.
This is a work in progress, so be sure to read the preface (which highlights some of the issues with this document). If you find any errors, please comment below.
Download
FunctionalEquationReference_v1_1.pdf (175 KB).
Tags: AI, binomial transform, difference equation, discrete calculus, functional equation, functional equations, Mathematics, z-transform
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