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math.GM2025
Complete Monotonicity of the function involving derivatives of Barnes G-function
Deepshikha Mishra, A. Swaminathan
In this manuscript, we present the complete monotonicity of functions defined in terms of the poly-double gamma function \begin{align*} ψ_2^{(n)}(x) = (-1)^{n+1} n! \sum_{k=0}^{\in…
math.GM2025
Inequalities involving a Ramanujan Integral
Deepshikha Mishra, A. Swaminathan
In this manuscript, various properties of the Ramanujan integral , defined as \begin{align*} I_R(x) = \int_0^\infty e^{-xt} \dfrac{dt}{t(π^2 + \log^2 t)}, \quad x>0, \end{a…
math.CV2025
Integral representation and functional inequalities involving generalized polylogarithm
Deepshikha Mishra, A. Swaminathan
The purpose of this manuscript is to derive two distinct integral representations of the generalized polylogarithm using two different techniques. The first approach involves the D…