S. Jha

activity

20192026

most citedVerifiable Natural Language to Linear Temporal Logic Translation: A Benchmark Dataset and Evaluation Suite

3 citations · 5 across the 13 of their papers we have counts for

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6 papers · 1 filter

math.GM2026

A Four-Genus Kronecker-Limit Evaluation of the Alternating Rogers-Ramanujan Continued Fraction

Sumit Kumar Jha

We evaluate the six odd class-number-four cases left unevaluated in Ramanathan's treatment of the Rogers-Ramanujan continued fraction. Let \[ S(q)=-R(-q),\qquad R(q)=\cfrac{q^{1/5}…

math.GM2020

A formula for the number of partitions of $n$ in terms of the partial Bell polynomials

Sumit Kumar Jha

We derive a formula for $p (n)$ (the number of partitions of $n$ ) in terms of the partial Bell polynomials using Faà di Bruno's formula and Euler's pentagonal number theorem.

math.GM2020

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 $n$ in terms of Bell polynomials and Stirling numbers of the second kind using the Faà di Bruno's formula.

math.GM2020

An identity involving Bernoulli numbers and the Stirling numbers of the second kind

Sumit Kumar Jha

Let $B_{n}$ denote the Bernoulli numbers, and $S (n, k)$ denote the Stirling numbers of the second kind. We prove the following identity $$ B_{m+n}=\sum_{\substack{0\leq k \leq n \\…

math.GM2020

On the Mellin transform of $\frac{l o g ^{n} ( 1 + x )}{( 1 + x ) ^{m + 1}}$

Sumit Kumar Jha

We use the Ramanujan's master theorem to evaluate the integral $\int_{0}^{\infty} \frac{x ^{l - 1}}{( 1 + x ) ^{m + 1}} lo g^{n} (1 + x) d x$ in terms of the digamma function, the gamma functi…

math.GM2019

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…

A Four-Genus Kronecker-Limit Evaluation of the Alternating Rogers-Ramanujan Continued Fraction

A formula for the number of partitions of n in terms of the partial Bell polynomials

A closed form for the generalized Bernoulli polynomials via Faà di Bruno's formula

An identity involving Bernoulli numbers and the Stirling numbers of the second kind

On the Mellin transform of (1+x)m+1logn(1+x)​

Two new explicit formulas for the Bernoulli Numbers

A formula for the number of partitions of $n$ in terms of the partial Bell polynomials

On the Mellin transform of $\frac{l o g ^{n} ( 1 + x )}{( 1 + x ) ^{m + 1}}$