The primitive function for slit-height desmearing in SAXS

The recursive method of Schmidt & Fedorov [J. Appl. Cryst. (1978). 11, 411–416] allows for calculation of the correction function g(t) for slit-height smearing in terms of the slit transmission function f(t). In this method, if the primitive function g(t) = g₀(t) is known for the interval 0 ≤ t ≤ t₀, then g(t) = g_n(t) can be calculated recursively, for the intervals n^½t₀ ≤ t ≤ (n + 1)^½t₀. A general method is presented for calculating g₀(t) in powers of t. To illustrate the utility of our method, three numerical examples are examined, indicating rapid convergence to a level of accuracy of 1 in 10⁶.