The paper offers a study of the inverse Laplace transforms of the functions $I_n(rs)\{sI_n^{'}(s)\}^{-1}$ where $I_n$ is the modified Bessel function of the first kind and $r$ is a parameter. The present study is a continuation of the author's previous work %[\textit{Canadian Mathematical Bulletin} 45] on the singular behavior of the special case of the functions in question, $r$=1. The general case of $r \in [0,1]$ is addressed, and it is shown that the inverse Laplace transforms for such $r$ exhibit significantly more complex behavior than their predecessors, even though they still only have two different types of points of discontinuity: singularities and finite discontinuities. The functions studied originate from non-stationary fluid-structure interaction, and as such are of interest to researchers working in the area.

MSC Classifications:

44A10, 44A20, 33C10, 40A30, 74F10, 76Q05 show english descriptions Laplace transform
Transforms of special functions
Bessel and Airy functions, cylinder functions, ${}_0F_1$
Convergence and divergence of series and sequences of functions
Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
Hydro- and aero-acoustics 44A10 - Laplace transform
44A20 - Transforms of special functions
33C10 - Bessel and Airy functions, cylinder functions, ${}_0F_1$
40A30 - Convergence and divergence of series and sequences of functions
74F10 - Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76Q05 - Hydro- and aero-acoustics

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