On the non homogeneous quadratic Bessel zeta function

Details On the non homogeneous quadratic Bessel zeta function On the non homogeneous quadratic Bessel zeta function

2003-12-06

arxiv.org/abs/math-ph/0312020v1

Physics

Mathematical Physics

Scientific paper

We study the non homogeneous quadratic Bessel zeta function
$\zeta_{RB}(s,\nu,a)$ defined as the sum of the square of the positive zeros of
the Bessel function $J_\nu(z)$ plus a positive constant. In particular, we give
explicit formulas for the main associated zeta invariants, namely poles and
residua, $\zeta_{RB}(0,\nu,a)$ and $\zeta'_{RB}(0,\nu,a)$.

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