Relative extrema of Legendre functions of the second kind (Q912257)

Legendre functions of the second kind, \(Q_ n(x)\), satisfy many of the same properties that Legendre polynomials \(P_ n(x)\) satisfy. A few identities are proved here, and then used to show that the relative extrema of \(| Q_ n(x)|\) are decreasing functions of the degree when they are ordered from 1 back to -1. The Legendre polynomial result was proved by Szegö forty years ago.