“A” is for Airy, “B” is for…

Earlier today, while hacking my way with A. Saha through Gradshteyn-Rizhik in search of some clue to an integral he wanted to compute, we found a close enough approximation where, on the right-hand side, a function Dp appeared. I had no idea what it could possibly be; the lack of an index meant we had to go through the whole back section on special functions to locate it (it turns out to be a “parabolic cylinder function”, a close relative of Whittaker functions and of confluent hypergeometric functions).

This led me to wonder if one could make a whole alphabet song of special functions: is there a letter, poor thing, such that no well-known special function is named after it? (I’m allowing multi-letter names, so that “A” goes with the Airy function Ai(z)). I’m not even sure about B, though some Bessel function should fit…

As I’ve just lent my copy of G-R, I can’t look right away. But aspiring song-writers can start looking and suggesting catchy rhymes and couplets to go with the long overdue “Song of special functions”

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I am a professor of mathematics at ETH Zürich since 2008.

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