1. A monotonic property of Bessel functions,Journal of the London Mathematical Society,12 (1937), pp. 180–185.
2. Ch. Sturm, Sur les équations différentielles linéaires de deuxième ordre,Journal de Mathématiques pures et appliquées 1 (1836), pp. 106–186, esp. p. 179.
3. G. Szegő, Inequalities for the zeros of Legendre polynomials and related functions,Transactions of the American Mathematical Society,39 (1936), pp. 1–17.
4. We assume of course the existence of at least three zeros in (x 0,X 0).
5. I oweI. Bihari this remark. The present proof ofSonin's theorem requires partly less stringent restrictions onf(x) than the usual proof. SeeG. Szegő,Orthogonal polynomials (New York, 1939), p. 161, where it is assumed thatf(x)>0 ifx 0