On Legendre numbers of the second kind (Q1114731)

The Legendre numbers are constant terms of the functions in the fundamental system of solutions of Legendre's associated differential equation \[ \{(1-x^ 2)D^ 2-2xD+n(n+1)-m^ 2/(1-x^ 2)\}y=0, \] m and n non-negative integers. The author proves a number of basic properties of the Legendre numbers of the second kind, finds a connecting formula to Legendre numbers of the first kind, and proves convergence results for series of Legendre numbers.