Recurrent relations for the solutions of an infinite system of linear algebraic equations

• Date: 1995
• Main Authors: Gomilko, A. M., Гомилко, А. М.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1995
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5534
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We obtain recurrent relations for bounded solutions of the system of equations $$X_k - \sum\limits_{n = 0}^\infty {\frac{{(k + n)!}}{{k!n!}}} \alpha ^{k + n + 1} x_n = f_{k,} k = 0,1,..., \alpha \in (0,1/2),$$ with right-hand sides {f k } k=0 ∞ ={δ kj } k=0 ∞ ,j=0,1,..., where δ kj is the...