CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

On the Singular Behavior of the Inverse Laplace Transforms of the Functions $\frac{I_n(s)}{s I_n^\prime(s)}$

  Published:2002-09-01
 Printed: Sep 2002
  • Serguei Iakovlev
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
Format:   HTML   LaTeX   MathJax   PDF   PostScript  

Abstract

Exact analytical expressions for the inverse Laplace transforms of the functions $\frac{I_n(s)}{s I_n^\prime(s)}$ are obtained in the form of trigonometric series. The convergence of the series is analyzed theoretically, and it is proven that those diverge on an infinite denumerable set of points. Therefore it is shown that the inverse transforms have an infinite number of singular points. This result, to the best of the author's knowledge, is new, as the inverse transforms of $\frac{I_n(s)}{s I_n^\prime(s)}$ have previously been considered to be piecewise smooth and continuous. It is also found that the inverse transforms have an infinite number of points of finite discontinuity with different left- and right-side limits. The points of singularity and points of finite discontinuity alternate, and the sign of the infinity at the singular points also alternates depending on the order $n$. The behavior of the inverse transforms in the proximity of the singular points and the points of finite discontinuity is addressed as well.
MSC Classifications: 65R32, 44A10, 44A20, 74F10 show english descriptions Inverse problems
Laplace transform
Transforms of special functions
Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
65R32 - Inverse problems
44A10 - Laplace transform
44A20 - Transforms of special functions
74F10 - Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
 

© Canadian Mathematical Society, 2014 : http://www.cms.math.ca/