A Pincherle Theorem for Matrix Continued Fractions

Pincherle theorems equate convergence of a continued fraction to existence of a recessive solution of the associated linear system. Matrix continued fractions have recently been used in the study of singular potentials in high energy physics. The matrix continued fractions and discrete Riccati equations previously studied by the author, which were motivated by discrete control theory, had symplectic coefficient matrices. However, the matrix continued fractions employed by Znojil do not have symplectic structure. The previous definition of a recessive solution is modified to allow extension of the Pincherle theorem to include a wider class of continued fractions.