Tales from the ArXiv: "Bourgeois Functions"

The snippet below, from this new paper makes me wonder about a rigorous definition of a "bourgeois function"... 🤔

You Wouldn't Like These Functions When They're Angry

There is a family of special functions called Anger functions. You wouldn't like them when they're angry.

Here is the context: Physics Today has agreed to publish an obituary for Norman Zabusky, so I needed to find some information that they require to be part of it. This led me to Norman's PhD thesis, which I found online. It briefly mentions something called Lommel polynomials, with which I wasn't familiar. The definition in a thesis appendix was terse — it's not exactly an important part of the thesis — so I looked at Wikipedia, and I kept seeing links to special functions that weren't familiar to me, and I have followed a couple of them. Anger functions are one family.

These various special functions are closely related to Bessel functions.

"Numerical Methods for the Computation of the Confluent and Gauss Hypergeometric Functions"

My paper on computation of confluent and Gauss hypergeometric functions, from a project that started in Spring 2009, finally is not only out in a journal but now even has coordinates (volume, page numbers, etc.) Here are the details.

Title: Numerical Methods for the Computation of the Confluent and Gauss Hypergeometric Functions

Authors: John W. Pearson, Sheehan Olver, and Mason A. Porter

Abstract: The two most commonly used hypergeometric functions are the confluent hypergeometric function and the Gauss hypergeometric function. We review the available techniques for accurate, fast, and reliable computation of these two hypergeometric functions in different parameter and variable regimes. Themethods that we investigate include Taylor and asymptotic series computations, Gauss–Jacobi quadrature, numerical solution of differential equations, recurrence relations, and others. We discuss the results of numerical experiments used to determine the best methods, in practice, for each parameter and variable regime considered. We provide "roadmaps" with our recommendation for which methods should be used in each situation.

Our Matlab code is available from this website.