Construction of solutions of a partial differential equation with constant coefficients using the form of formal Series. III (Q1901204)

The paper is a continuation of two preceding articles by the same authors [part I: ibid. 31, No. 3, 411-419 (1991; Zbl 0735.35029); part II: ibid. 34, No. 2, 139-148 (1994; Zbl 0835.35023)] in investigation of classes \(F^{(- r)}_{xy}\) of formal series. One of the conclusions is the following theorem: The regular equation \(\sum_{nk+ ml= d} a_{kl} D^k_x D^l_y u(x, y)= 0\), where \(d= pmn\), has \(p\) linearly independent solutions in the class \(F^{(- 1)}_{xy}\).