On special orthogonal eigenfunctions and eigenfunction expansions
Michael D. Phillips · International Journal of Mathematical Education in Science and Technology · 1996
We extend some earlier results while illustrating solution techniques commonly encountered by students in undergraduate and beginning graduate courses of mathematical analysis, differential equations, and engineering mathematics. Previously, Turan's inequality was established by using a technique known as the Prüfer substitution. In the process of proving Turan's inequality, the existence of an infinite set of eigenvalues λk and a corresponding infinite set of eigenfunctions ϕ(x, kk )which satisfied a certain differential equation were established. The purpose of this paper is to extend these results by further establishing the properties of orthogonality and completeness using solution techniques and strategies commonly encountered by students in advanced mathematical courses.