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For a fixed prime p, Murty and Saradha (Acta Arith 133:349–362, 2008) studied the transcendental nature of special values of the p-adic digamma function, denoted as ψ p (r / p) + γ p . This research was later extended by Chatterjee and Gun in 2014, who investigated the case of ψ p (r / p n) + γ p , for any integer n > 1 . In this article, we generalize their results for distinct prime powers and explore the transcendental nature of the p-adic digamma values, with at most one exception. Further, we investigate the multiplicative independence of cyclotomic numbers satisfying certain conditions. Using this, we prove the transcendental nature of p-adic digamma values corresponding to ψ p (r / p q) + γ p , where p, q are distinct primes. [ABSTRACT FROM AUTHOR]

Let k , t be coprime integers, and let 1 ≤ r ≤ t. We let D k × (r , t ; n) denote the total number of parts among all k -indivisible partitions (i.e., those partitions where no part is divisible by k) of n which are congruent to r modulo t. In previous work of the authors [3] , an asymptotic estimate for D k × (r , t ; n) was shown to exhibit unpredictable biases between congruence classes. In the present paper, we confirm our earlier conjecture in [3] that there are no "ties" (i.e., equalities) in this asymptotic for different congruence classes. To obtain this result, we reframe this question in terms of L -functions, and we then employ a nonvanishing result due to Baker, Birch, and Wirsing [1] to conclude that there is always a bias towards one congruence class or another modulo t among all parts in k -indivisible partitions of n as n becomes large. [ABSTRACT FROM AUTHOR]

An open problem about integral representation of , proposed recently by Pain (2023), is resolved by integration by parts. More general integrals are examined by manipulating the beta integral and digamma function. [ABSTRACT FROM AUTHOR]

In this paper, we solve the question completely raised by Feng Qi and Dongkyu Lim in paper "Monotonicity properties for a ratio of finite many gamma functions" published in Advances in Difference Equations and get some properties about ratios of finitely many gamma functions such as complete monotonicity, logarithmically complete monotonicity, the Bernstein function property, null point and extreme value. [ABSTRACT FROM AUTHOR]

In this paper, a new approximation formula for the gamma function and some of its symmetric inequalities are established. We prove the superiority of our results over Yang and Tian's approximation formula for the gamma function of order v − 9 . [ABSTRACT FROM AUTHOR]

In this note, we prove that x n 1 - e - x (n) > 0 for all x ∈ (log 2 , ∞) and n ∈ N . This result improves a theorem of Al-Musallam and Bustoz (Ramanujan J 11:399–402, 2006). [ABSTRACT FROM AUTHOR]

In this paper, a new approximation formula for the gamma function and some of its symmetric inequalities are established. We prove the superiority of our results over Yang and Tian’s approximation formula for the gamma function of order v−9.

We propose closed form estimators for the most popular bivariate beta distribution known to date and derive their asymptotic variances. The asymptotic properties of the proposed estimators are compared to asymptotic properties of the maximum likelihood estimators. The proposed estimators can have smaller asymptotic variances and smaller asymptotic covariances compared to maximum likelihood estimators. [ABSTRACT FROM AUTHOR]