Talk:Bessel equation

From Encyclopedia of Mathematics
Jump to: navigation, search

Remark: One of our readers observed that the equation after eq. (4) was not correct on this preceding version, therefore this has been corrected. It should as well be checked if this change is compatible with the subsequent formulae (Lommel, Struve, Anger, Weber function). --Ulf Rehmann 23:14, 20 February 2014 (CET)

Hello Ulf, all checked and texxed. Actually none of the pages was affected by the same mistake, which must therefore have been a local typo. The page on Struve functions did contain some other small mistakes though. Now, reading more carefully all these pages, I discovered that one major source of confusion might be the following: the cylinder functions $Y_\nu$, which are commonly called Bessel functions of second type, in most of our entries are instead denoted by $N_\nu$ and called
  • cylinder functions of second type
  • or Neumann functions
  • or Weber functions.

It is historically a correct choice since they were indeed introduced by Neumann and Weber... but on the other hand the entry Weber function is about a different class of functions, which are the one usually called Weber functions. Thus sometimes Weber function is not linked appropriately. For the moment I reverted to the current terminology and notation the pages Anger function, Bessel functions, Bessel equation, Lommel function, Struve function and Weber function. With time I will take care of Cylinder functions, Hankel functions and Neumann function. If anybody sees some inconsistencies, please send me a message. Camillo (talk) 10:24, 22 February 2014 (CET)

Indeed, on the page Cylinder functions, the notations $N_\nu, Y_\nu$ are switched "inline", see, e.g., after equations (5) and (8) on that page. That should all be straightend out.--Ulf Rehmann 21:35, 24 February 2014 (CET)
Hah, I did not notice that: pretty weird! Anyway, I find the book of Watson extremely well written, precise and simple to use as a reference: I am mainly following it when I restyle the existing pages. Camillo (talk) 14:39, 26 February 2014 (CET)
I have texxed and adjusted the notation in all the pages mentioned above Camillo (talk) 18:11, 2 April 2014 (CEST)

Thanks to User:Bo.hoffmann for fixing an error not noted since Feb 2014. Boris Tsirelson (talk) 19:48, 3 March 2015 (CET)

How to Cite This Entry:
Bessel equation. Encyclopedia of Mathematics. URL: