On a G. Boole’s Identity for Rational Functions and Some Trace Formulas

In 1857 George Boole found an identity for a class of rational functions, which for a given function, connects the sum of its residues at finite points with the difference between the sums of its zeros and poles. We consider generalizations of this identity to the case of Nevanlinna functions. We apply these results to obtain some new trace formulas for infinite Jacobi matrices and for differential operators of the second order.