In this paper, by the Riordan array method, we show that in Ramanujan's asymptotic
expansion of the harmonic numbers, the coefficients given by Villarino satisfy the recurrence …

In this paper, we investigate certain asymptotic series used by Hirschhorn to prove an
asymptotic expansion of Ramanujan for the n th harmonic number. We give a general form …

In this paper, we provide the coefficients of the Ramanujan expansion proposed by Wang
[23] with a different method. Then, we present the rates of convergence of the expansion for …

In this paper, we provide a method for constructing a continued fraction approximation
based on a given asymptotic expansion. We establish some asymptotic expansions for the …

In this paper, we establish three (general) asymptotic expansions of the Ramanujan type for
the harmonic numbers, and give the corresponding recurrences of the coefficient sequence …

Ramanujan’s Harmonic Number Expansion and Two Identities for Bernoulli Numbers Page 1
Results Math 72 (2017), 1857–1864 c© 2017 Springer International Publishing AG 1422-6383/17/041857-8 …

We establish a new combinatorial identity related to the well-known Bernoulli numbers,
which generalizes the result due to Feng and Wang. By means of the identity, we find a …

On the Ramanujan’s harmonic number expansion Page 1 Ramanujan’s harmonic number
expansion Kwang-Wu Chen Euler’s asymptotic expansion Ramanujan’s asymptotic expansion …

In this paper, we present various asymptotic series for the harmonic number H_n= ∑ _ k= 1^
n 1 k H n=∑ k= 1 n 1 k. For example, we give a pair of recurrence relations for determining …

Similar to Ramanujan's expansion for the n th harmonic number, Villarino suggested that
there might exist a series expansion for the logarithm of the factorial in terms of the …