Logarithmic convexity and increasing property of the Bernoulli numbers and their ratios

Complete Monotonicity for a New Ratio of Finitely Many Gamma Functions

“…see also [26,44,50,56] and closely related references therein. In July 2021, an anonymous referee pointed out that the function F ρ,θ (x) defined in (1.8) satisfies that…”

Parametric kinds of generalized Apostol--Bernoulli polynomials and their properties

“…Then, Tom M. Apostol developed Bernoulli polynomials in [2]. Later, some properties and relations related to these polynomials are obtained [5,9,10,11,19,20,26,27,28,29,30,31,32,33,34,35,37].…”

“…The quantities B n (0) = B n are called the Bernoulli numbers. Due to that the function In [26,37], some new properties for the ratio B2n+2 B2n with n ∈ N were discovered. One of the relations between the Bernoulli numbers and polynomials is…”

Several Double Inequalities for Integer Powers of the Sinc and Sinhc Functions with Applications to the Neuman–Sándor Mean and the First Seiffert Mean

“…In the recent papers [27][28][29], some novel results for the even-indexed Bernoulli numbers B 2n were discovered. Lemma 3 ([30]).…”