Polynomials of Transfer Functions with Poles Only Satisfying Conditions at the Origin

The Butterworth polynomials, which satisfy amplitude conditions only at the origin, and the Bessel polynomials, which satisfy phase conditions only, are shown to be the extreme cases of a more general class of polynomials, which can be listed in a two-dimensional array, and which satisfy both amplitude and phase conditions. These polynomials are listed up to the seventh order, and a few general formulas are given which permit us to calculate these polynomials along certain lines of the two-dimensional array for any given order.