5 papers
A closed form for the generalized Bernoulli polynomials via Faà di Bruno's formula
Sumit Kumar Jha
We derive a closed form for the generalized Bernoulli polynomial of order in terms of Bell polynomials and Stirling numbers of the second kind using the Faà di Bruno's formula.
An identity involving Bernoulli numbers and the Stirling numbers of the second kind
Sumit Kumar Jha
Let denote the Bernoulli numbers, and denote the Stirling numbers of the second kind. We prove the following identity $$ B_{m+n}=\sum_{\substack{0\leq k \leq n \\…
Two new identities involving the Bernoulli numbers, the Euler numbers, and the Stirling numbers of the first kind
Sumit Kumar Jha
We derive two new identities involving the Bernoulli numbers, the Euler numbers, and the Stirling numbers of the first kind using analytic continuation of a well known identity for…
On the Mellin transform of
Sumit Kumar Jha
We use the Ramanujan's master theorem to evaluate the integral in terms of the digamma function, the gamma functi…
Two new explicit formulas for the Bernoulli Numbers
Sumit Kumar Jha
In this brief note, we give two explicit formulas for the Bernoulli Numbers in terms of the Stirling numbers of the second kind, and the Eulerian Numbers. To the best of our knowle…