Scripts for the Ismail-Letessier-Askey (ILA) monotonicity conjecture for zeros of ultraspherical polynomials

<p>A number of conjectured monotonicity properties for zeros of ultraspherical polynomials are reviewed, leading up to the ILA conjecture of the title, which has been proved in 1999 by Elbert and Siafarikas. It is shown that two of the earlier conjectures are consequences of the ILA conjecture. Computational support is provided for strengthening several of these conjectures, including the ILA conjecture, from monotonicity to complete monotonicity.</p>