Demonstratio Mathematica (Jul 2023)

Increasing property and logarithmic convexity of functions involving Dirichlet lambda function

  • Qi Feng,
  • Lim Dongkyu

DOI
https://doi.org/10.1515/dema-2022-0243
Journal volume & issue
Vol. 56, no. 1
pp. 964 – 975

Abstract

Read online

In this article, with the help of an integral representation of the Dirichlet lambda function, by means of a monotonicity rule for the ratio of two integrals with a parameter, and by virtue of complete monotonicity and another property of an elementary function involving the exponential function, the authors find increasing property and logarithmic convexity of two functions containing the gamma function and the Dirichlet lambda function.

Keywords