On series of orthogonal polynomials and systems of classical type polynomials

• Date: 2021
• Main Authors: Zagorodnyuk, S. M., Zagorodnyuk, Sergey, Загороднюк , С. М.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2021
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/6527
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.587 If $\displaystyle\sum\nolimits_{k=0}^\infty c_k g_k(x),$ is a formal series of orthonormal polynomials $g_k(x)$ on the real line that has positive coefficients $c_k,$ then its partial sums $u_n(x)$ are associated with Jacobi type pencils.Therefore, they possess a recurrence relation and...