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In marching-on-in-degree time domain method of moment, the transient responses are often expanded by a finite number of associated Laguerre functions. There is an error associated in truncating the associated Laguerre function series beyond that what is necessary in the solution process. This error is related to the scaling factor used in the argument of the associated Laguerre functions that actually approximates the unknown temporal variations. A least upper bound of this error is deduced. Based on this bound, one can obtain an optimum scaling factor to minimize this error so that it is guaranteed to be below a certain bound.