The zeta function for the triangular potential

The zeta functions for the Schr\"odinger equation with a triangular potential are investigated. Values of computed using both Weierstrass factorization theorem and analytic continuation via contour integration. results were found to be consistent where domains two methods overlap. Analytic is used compute values at zero negative integers, explore pole structure (and residue values), as well value slopes origin. Those computation trace determinant associated Hamiltonians.