In this paper, by deriving an inequality involving the generating function of Bernoulli numbers, author introduces a new ratio finitely many gamma functions, finds complete monotonicity second logarithmic derivative ratio, and simply reviews several linear combinations digamma or trigamma functions.

Motivated by several conjectures posed in the paper "F. Qi and A.-Q. Liu, Completely monotonic degrees for a difference between logarithmic psi functions, J. Comput. Appl. Math., vol. 361, pp. 366--371 (2019); available online at https://doi.org/10.1016/j.cam.2019.05.001", authors compute completely of remainders asymptotic expansions logarithm gamma function digamma function.

The sums of three trigonometric series with logarithmic coefficients are derived by extending an approach first utilized Lerch. By applying Frullani's theorem to two these series, non-trivial integrals involving hyperbolic functions evaluated in terms the digamma function.

We give an overview of the use of asymptotic expansions of gamma and related functions — ratio of gamma functions, powers, digamma and polygamma functions. The aim is to introduce a general theory which can unify various particular formulas for factorial functions and binomial coefficients. The connection with inequalities for gamma function is established. Also, a systematic approach to asympt...

In this paper, we introduce 3-dimensional L−summing method, which is a rearrangement of the summation P Aabc with 1 ≤ a, b, c ≤ n. Applying this method on some special arrays, we obtain some identities on the Riemann zeta function and digamma function. Also, we give a Maple program for this method to obtain identities with input various arrays and out put identities concerning some elementary f...

The Barnes’ G-function G(x) = 1/Γ2, satisfies the functional equation log G(x + 1) − log G(x) = log Γ(x). We complement W. Krull’s work in Bemerkungen zur Differenzengleichung g(x + 1)− g(x) = φ(x), Math. Nachrichten 1 (1948), 365-376 with additional results that yield a different characterization of the function G, new expansions and sharp bounds for G on x > 0 in terms of Gamma and Digamma fu...