Came across another interesting sum when trying to use Euler-Maclaurin on the ratio of a geometric series.
Does anyone recognize a closed form to the following?:
$$ \sum_{z=1}\frac{B_{2z}\ x^{2z}}{(2z)!(2z+2m)!}\ s.t. m \in \mathbb N = ??? $$
I have some clues, namely:
https://mathworld.wolfram.com/BernoulliNumber.html
Also, the idea of Eqtn 42 from: https://mathworld.wolfram.com/BesselFunctionoftheFirstKind.html which more information on can be found: https://en.wikipedia.org/wiki/Bessel_function