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math.NT2024
Mneimneh-type Binomial Sums of Multiple Harmonic-type Sums
Ende Pan, Ce Xu
In this paper, we establish some expressions of Mneimneh-type binomial sums involving multiple harmonic-type sums in terms of finite sums of Stirling numbers, Bell numbers and some…
math.NT2024
General Mneimneh-type Binomial Sum involving Harmonic Numbers
Ende Pan, Ce Xu
Recently, Mneimneh proved the remarkable identity \begin{align*} \sum_{k=0}^n H_k\binom{n}{k} p^k(1-p)^{n-k}=\sum_{i=1}^n \frac{1-(1-p)^i}{i}\quad (p\in [0,1]) \end{align*} as the…