Weighting coefficients for certain maximally flat nonrecursive digital filters

The weighting coefficients for maximally flat nonrecursive digital ruters have been derived for low-pass filters having equal passband and stopband widths. The solution is in closed form and can be readily evaluated even for large filter order. Asymptotically the coefficients of the finite series expansion converge to the Fourier series coefficients. Hilbert transformers and decimation filters are among the suggested applications for this form of filter.