Robert E. Gaunt

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20182022

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math.CA2021

Bounds for an integral involving the modified Struve function of the first kind

Robert E. Gaunt

Simple upper and lower bounds are established for the integral $\int_{0}^{x} e^{- β t} t^{ν} L_{ν} (t) d t$ , where $x > 0$ , $ν > - 1$ , $0 < β < 1$ and $L_{ν} (x)$ is the…

math.CA2020

Bounds for an integral of the modified Bessel function of the first kind and expressions involving it

Robert E. Gaunt

Simple upper and lower bounds are obtained for the integral $\int_{0}^{x} e^{- γ t} t^{ν} I_{ν} (t) d t$ , $x > 0$ , $ν > - \frac{1}{2}$ , $0 < γ < 1$ . Most of our bounds for this integral…

math.CA2019

Inequalities for some integrals involving modified Lommel functions of the first kind

Robert E. Gaunt

In this paper, we obtain inequalities for some integrals involving the modified Lommel function of the first kind $t_{μ, ν} (x)$ . In most cases, these inequalities are tight in certa…

math.CA2019

Bounds for modified Lommel functions of the first kind and their ratios

Robert E. Gaunt

The modified Lommel function $t_{μ, ν} (x)$ is an important special function, but to date there has been little progress on the problem of obtaining functional inequalities for $t_{μ…

math.CA2018

Inequalities for integrals of the modified Struve function of the first kind II

Robert E. Gaunt

Simple inequalities are established for integrals of the type $\int_{0}^{x} e^{- γ t} t^{- ν} L_{ν} (t) d t$ , where $x > 0$ , $0 \leq γ < 1$ , $ν > - \frac{3}{2}$ and $\mathb…

math.CA2018

Inequalities for some integrals involving modified Bessel functions

Robert E. Gaunt

Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases these inequalities are tight in certain l…