The Complementary <i>q</i>-Lidstone Interpolating Polynomials and Applications

Abstract

In this paper, we introduce the complementary q-Lidstone interpolating polynomial of degree 2 n , which involves interpolating data at the odd-order q-derivatives. For this polynomial, we will provide a q-Peano representation of the error function. Next, we use these results to prove the existence of solutions of the complementary q-Lidstone boundary value problems. Some examples are included.

Keywords

• <i>q</i>-Lidstone polynomials
• <i>q</i>-Peano’s theorem
• complementary <i>q</i>-Lidstone
• boundary value problems