On Continued Fractions and Their Applications
On Continued Fractions and Their Applications作者机构：Department of Mathematics Faculty of Science University of Tripoli Tripoli Libya
出 版 物：《Journal of Applied Mathematics and Physics》 (应用数学与应用物理（英文）)
年 卷 期：2022年第10卷第1期
页 面：142-159页
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
主 题：Continued Fraction Equation Numerical Method Roots Series Finite
摘 要：Continued fractions constitute a very important subject in mathematics. Their importance lies in the fact that they have very interesting and beautiful applications in many fields in pure and applied sciences. This review article will reveal some of these applications and will reflect the beauty behind their uses in calculating roots of real numbers, getting solutions of algebraic Equations of the second degree, and their uses in solving special ordinary differential Equations such as Legendre, Hermite, and Laguerre Equations;moreover and most important, their use in physics in solving Schrodinger Equation for a certain potential. A comparison will also be given between the results obtained via continued fractions and those obtained through the use of well-known numerical methods. Advances in the subject will be discussed at the end of this review article.
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