Expansions in Series of Homogeneous Polynomial Solutions of the General Two-Dimensional Linear Partial Differential Equation of the Second Order with Constant Coefficients

摘要

This line may vary from one series to another but may be arbitrary (not a characteristic). Finally, we show that the Taylor (double) series expansion about the origin of u(x,y) the sum of (l.l), converges in the largest parallelogram M|x| + |y| <ρ included in the region of convergence of (l.l) and perhaps on portions of the extended diagonals. In the parabolic case the double series has only two rows and the parallelogram becomes the strip of convergence itself.