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

• 發表在: Mathematical and Computational Applications
• Main Authors: Zeinab Mansour, Maryam Al-Towailb
• 格式: Article
• 語言: 英语
• 出版: MDPI AG 2020-06-01
• 主題: <i>q</i>-Lidstone polynomials; <i>q</i>-Peano’s theorem; complementary <i>q</i>-Lidstone; boundary value problems
• 在線閱讀: https://www.mdpi.com/2297-8747/25/2/34
• ISSN: 1300-686X; 2297-8747

In this paper, we introduce the complementary <i>q</i>-Lidstone interpolating polynomial of degree <inline-formula> <math display="inline"> <semantics> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </semantics> </math> </inline-formula>, which involves interpolating data at the odd-order <i>q</i>-derivatives. For this polynomial, we will provide a <i>q</i>-Peano representation of the error function. Next, we use these results to prove the existence of solutions of the complementary <i>q</i>-Lidstone boundary value problems. Some examples are included.