String Jacobi matrices with very fast decreasing weights (Q1884743)

The aim of the present paper is to investigate a class of string, compact Jacobi matrices with very rapidly decreasing weights. The authors find the Hellinger-Weyl function representation as the ratio of two entire functions with known Taylor series representation and, furthermore, asymptotic estimations of the zeroes of these entire functions and of the eigenvalues of a corresponding operator. Finally, they apply this theory to Rogers-Ramanujan functions.