Browsing by Subject "Lommel functions"

Now showing items 1-3 of 3

    • Article  

      On the log-concavity of the fractional integral of the sine function 

      Koumandos, S. (2016)
      We prove that the function Fλ(x):=∫0x(x−t)λsintdt is logarithmically concave on (0,∞) if and only if λ≥2. As a consequence, a Turán type inequality for certain Lommel functions of the first kind is obtained. Furthermore, ...
    • Article  

      Positive Trigonometric Integrals Associated with Some Lommel Functions of the First Kind 

      Koumandos, S. (2017)
      We prove that (Formula Presented.), for all μ≥ 1 / 2 and x≥ π, where sμ,12(x) is the Lommel function of the first kind. This refines a result of Steinig published in 1972. As an application, we derive positive functional ...
    • Article  

      The zeros of certain Lommel functions 

      Koumandos, S.; Lamprecht, M. (2012)
      Lommel's function s μ,ν(z) is a particular solution of the differential equation z 2y″ + zy′ + (z 2 - ν 2)y = z μ+1. Here we present estimates and monotonicity properties of the positive zeros of s μ-1/2,1/2(z) when μ ∈ ...