... Publishing CorporationJournal of Inequalities and ApplicationsVolume 2010, Article ID 816363, 29 pagesdoi:10.1155/2010/816363 Research Article Derivatives of Orthonormal Polynomials and Coefficients ... Inequalities and Applications 25Proof of Theorem 4.4. To prove the result, we proceed by induction on i.From4.2 and 4.4we know that es,sl, m, k, n1/s! and the following recurrence relation; ... and 2.13.Journal of Inequalities and Applications 23Theorem 4.4. Let 0 ≤ s ≤ i ≤ m − 1. Then one has for |xkn|≤an/2|es,il, m, k, n|≤ Cnani−s.4.14 On the other hand,...