Coefficients for ´decomposition´ of functions into Laguerre-function series

Given a function of time which behaves arbitrarily up to a certain time and is thereafter negligible, a satisfactory 10-term Laguerre-series approximation to the function can in general be written down in terms of the values of the function (obtained by graphical interpolation if necessary) at times proportional to the 10 zeros of the Laguerre function of order 10. The way in which the approximation fails when the procedure is deliberately applied to an unsuitable function is considered.