calculus - Closed form for $sum_{n=1}^{infty}frac{(-1)^n}{sqrt{n^2+a^2}}$

Do the convergent sum

$$\sum_{n=1}^{\infty}\frac{(-1)^n}{\sqrt{n^2+a^2}}$$

posses a closed form? ($a \in \mathbb{R}$)

Special case is known, for $a=0$ one recalls well known alternating harmonic series :

$$\sum_{n=1}^{\infty}\frac{(-1)^n}{n}=-\ln 2$$