A representation for Jost solutions and an efficient method for solving the spectral problem on the half line

2019 ◽  
Vol 43 (16) ◽  
pp. 9304-9319 ◽  
Author(s):  
Briceyda B. Delgado ◽  
Kira V. Khmelnytskaya ◽  
Vladislav V. Kravchenko
Keyword(s):  
Spectral Problem ◽  
Efficient Method ◽  
Half Line ◽  
Jost Solutions

scholarly journals An extension of the method of brackets. Part 1

2017 ◽  
Vol 15 (1) ◽  
pp. 1181-1211 ◽  
Author(s):  
Ivan Gonzalez ◽  
Karen Kohl ◽  
Lin Jiu ◽  
Victor H. Moll
Keyword(s):  
Efficient Method ◽  
Blow Up ◽  
Divergent Series ◽  
Half Line ◽  
Definite Integrals ◽  
Small Collection ◽  
Formal Representations

Abstract The method of brackets is an efficient method for the evaluation of alarge class of definite integrals on the half-line. It is based on a small collection of rules, some of which are heuristic. The extension discussed here is based on the concepts of null and divergent series. These are formal representations of functions, whose coefficients an have meromorphic representations for n ∈ ℂ, but might vanish or blow up when n ∈ ℕ. These ideas are illustrated with the evaluation of a variety of entries from the classical table of integrals by Gradshteyn and Ryzhik.

Sign in / Sign up

Export Citation Format

Share Document