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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*} Ï_2^{(n)}(x) = (-1)^{n+1} n! \sum_{k=0}^{\i…
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(Ï^2 + \log^2 t)}, \quad x>0, \end{…