Closed Forms: What They Are Mathematics abounds in terms that are in frequent use yet are
rarely made precise. Two such are rigorous proof and closed form (absent the technical use …

S. Ramanujan introduced a technique, known as Ramanujan's Master Theorem, which
provides an explicit expression for the Mellin transform of a function in terms of the analytic …

We study the densities of uniform random walks in the plane. A special focus is on the case
of short walks with three or four steps and, less completely, those with five steps. As one of …

We find new representations, in terms of constant terms of powers of Laurent polynomials,
for all the 15 sporadic Apéry-like sequences discovered by Zagier, Almkvist-Zudilin and …

The hyper-Mahler measures $ m_k (1+ x_1+ x_2), k\in\mathbb Z_ {> 1} $ and $ m_k (1+
x_1+ x_2+ x_3), k\in\mathbb Z_ {> 1} $ are evaluated in closed form, via multiple …

We resolve a family of recently observed identities involving 1/π using the theory of modular
forms and hypergeometric series. In particular, we resort to a formula of Brafman which …

We investigate the moments of 3-step and 4-step uniform random walks in the plane. In
particular, we further analyze a formula conjectured in expressing 4-step moments in terms …

A small set of combinatorial sequences have coefficients that can be represented as
moments of a nonnegative measure on $[0,\infty) $. Such sequences are known as Stieltjes …

Using contour deformations and integrations over modular forms, we compute certain
Bessel moments arising from diagrammatic expansions in two-dimensional quantum field …

Pollard's rho algorithm, along with parallelized, vectorized, and negating variants, is the
standard method to compute discrete logarithms in generic prime-order groups. This paper …