Asymptotics of sums with Gaussian kernel and multiplicative coefficients

This study deals with the asymptotic behavior of finite sums containing a Gaussian function and a multiplicative term. Such sums naturally arise in complexity analysis of binary tree traversal and ray searching algorithms. Using the method of complex integration, we transform the discrete finite sum into an integral along an infinite vertical line in the complex plane. We demonstrate that the integrand contains a positive integer power of the Riemann zeta function. By applying standard residue calculation techniques, we obtain the asymptotic value of this integral.