Bessel functions are interesting and useful, but they’re surrounded by arcane terminology. It may seem that there are endless varieties of Bessel functions, but there are not that many variations and they are simply related to each other.

Each letter in the diagram is taken from the traditional notation for a class of Bessel functions. Functions in the same row satisfy the same differential equation. Functions in the same column have something in common in their naming.

The lines represent simple relations between functions. There’s one line conspicuously missing from the diagram, and that’s no accident.

These notes give the details behind the diagram.

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