Estimate of the error of depletion function expansion series

It is proved that the series into which depletion functions can be expanded will converge for all values of the depletion function arguments. An expression for the relative error caused by the series expansion is derived which depends on the number of series terms. It is shown that the evaluation of a depletion function with a large number of arguments via series expansion can be performed quite efficiently and to a good accuracy even in the case that the differences between the arguments of the function are small. As a result, even very long depletion chains can be analytically evaluated to a good accuracy. (orig.)