Acceleration of the convergence of the Laguerre series in the problem of inverting the Laplace transform

When the Laplace transform is inverted numerically, the original function is sought in the form of a series in the Laguerre polynomials. To accelerate the convergence of this series, the Euler–Knopp method is used. The techniques for selecting the optimal value of the parameter of the transform on the real axis and in the complex plane are proposed.