Talk:Hermite class

Questions

I have just created this article, but there are some things I don't understand.

In the Hadamard product, how does one define the infinite product if the sum of $|\Re {\frac {1}{z_{n}}}|$ doesn't converge?

That would cause trouble in the infinite product if there weren't the factor $1-z/z_{n}$. But with that it's all right, and de Branges in his book gives as an exercise (Problem 9, page 14) to show that this infinite product converges given the condition on the roots that $\sum _{n}{\frac {1-\operatorname {Im} z_{n}}{|z_{n}|^{2}}}<\infty$. Eric Kvaalen (talk) 07:40, 11 March 2014 (UTC)

Is the Bessel function $J_{0}(z)$ in the class?

Eric Kvaalen (talk) 16:37, 5 January 2013 (UTC)