Monotonicity properties of several functions involving the difference between the modified Bessel and Struve functions of the first kind

In this paper, we carry out a comprehensive research on the function Dν(x)=x−ν(Iν(x)−Lν(x)) for ν>−1/2 and x>0, which finds wide applications in various fields, where Iν(x) and Lν(x) are the modified Bessel function of the first kind and the modified Struve function, respectively. Specifically, we present some basic properties of the function x↦Dν(x), along with several useful bounds. Moreover, we establish the monotonicity of the bounded functions x↦xDν(x), x↦Dμ(x)/Dν(x), and x↦(Dν+1(x)+Dν−1(x))/Dν(x). Finally, numerical computations show that treating Dν(x) as a whole can avoid cancellation problems arising from the subtraction of two large numbers when x is extremely large.