Victor H. Moll
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Victor H. Moll has a total of 55 co-authors. Here are the top co-authors by number of shared publications:
- Atul Dixit
Department of Mathematics, Tulane University, New Orleans, USA
11 shared publications - Christophe Vignat
Department of Mathematics, Tulane University, New Orleans, USA
11 shared publications - Tewodros Amdeberhan
Department of Mathematics, Tulane University, New Orleans, USA
10 shared publications - Lin Jiu
Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, B3H 4R2, Canada
9 shared publications - Ivan Gonzalez
Instituto de Física y Astronomía Universidad de Valparaíso Avenida Gran Bretaña 1111 Valparaíso Chile
5 shared publications - Christophe Vignat
Department of Mathematics, Tulane University, New Orleans, LA 70118, USA
3 shared publications
Latest Publications
- Open Access
- 5 November 2025
- Published by Springer Nature in The Ramanujan Journal
- Vol. 68 (3) , 1-17
A monstrous integral
The method of brackets originated from the so-called negative dimension approach for evaluating definite integrals arising in Feynman diagrams. Its fundamental concept, still heuristic, identifies a bracket with a divergent integral. The method converts the integral into a bracket series and prescribes a concise set of rules for its evaluation. In this work we present a ten-variable monstrous integral that combines Bessel functions, polylogarithms, and the exponential integral, and we evaluate it exactly by means of the method of brackets. This example illustrates the flexibility and power of the technique.
- 5 November 2025
- Published by Springer Nature in The Ramanujan Journal
- Vol. 68 (3) , 1-17
Open AccessA monstrous integral
The method of brackets originated from the so-called negative dimension approach for evaluating definite integrals arising in Feynman diagrams. Its fundamental concept, still heuristic, identifies a bracket with a divergent integral. The method converts the integral into a bracket series and prescribes a concise set of rules for its evaluation. In this work we present a ten-variable monstrous integral that combines Bessel functions, polylogarithms, and the exponential integral, and we evaluate it exactly by means of the method of brackets. This example illustrates the flexibility and power of the technique.
- Open Access
Asymptotics and zeros of a special family of Jacobi polynomials
In this paper we study a family of non-classical Jacobi polynomials with varying parameters of the form $α_n=n+1/2$ and $β_n=-n-1/2$. We obtain global asymptotics for these polynomials, and use this to establish results on the location their zeros. The analysis is based on the Riemann Hilbert formulation of Jacobi polynomials derived from the non-hermitian orthogonality introduced by Kuijlaars, et al. This family of polynomials arise in the symbolic evaluation integrals in the work of Boros and Moll and corresponds to a limitting case, which is not considered in the works of Kuijlaars, et al. A remarkable feature in the analyisis is encountered when performing the local analysis of the RHP near the origin, where the local parametrix introduces a pole.Open AccessAsymptotics and zeros of a special family of Jacobi polynomials
In this paper we study a family of non-classical Jacobi polynomials with varying parameters of the form $α_n=n+1/2$ and $β_n=-n-1/2$. We obtain global asymptotics for these polynomials, and use this to establish results on the location their zeros. The analysis is based on the Riemann Hilbert formulation of Jacobi polynomials derived from the non-hermitian orthogonality introduced by Kuijlaars, et al. This family of polynomials arise in the symbolic evaluation integrals in the work of Boros and Moll and corresponds to a limitting case, which is not considered in the works of Kuijlaars, et al. A remarkable feature in the analyisis is encountered when performing the local analysis of the RHP near the origin, where the local parametrix introduces a pole. - Open Access
Symmetric tensor powers of graphs
The symmetric tensor power of graphs is introduced and its fundamental properties are explored. A wide range of intriguing phenomena occur when one considers symmetric tensor powers of familiar graphs. A host of open questions are presented, hoping to spur future research.
Open AccessSymmetric tensor powers of graphs
The symmetric tensor power of graphs is introduced and its fundamental properties are explored. A wide range of intriguing phenomena occur when one considers symmetric tensor powers of familiar graphs. A host of open questions are presented, hoping to spur future research.
- Open Access
- 9 September 2023
- Published by Elsevier in Physica D: Nonlinear Phenomena
- Vol. 456
Collisionless shock region of the KdV equation and an entry in Gradshteyn and Ryzhik
- 9 September 2023
- Published by Elsevier in Physica D: Nonlinear Phenomena
- Vol. 456
Open AccessCollisionless shock region of the KdV equation and an entry in Gradshteyn and Ryzhik
- Open Access
- 31 December 2022
- Published by Combinatorial Press in Online Journal of Analytic Combinatorics
- Vol. Issue 17, (17) , 1-10
Infinite log-convexity
Criteria to verify log-convexity of sequences is presented. Iterating this criteria produces infinitely log-convex sequences. As an application, several classical examples of sequences arising in Combinatorics and Special Functions are presented. The paper concludes with a conjecture regarding coefficients of chromatic polynomials.
- 31 December 2022
- Published by Combinatorial Press in Online Journal of Analytic Combinatorics
- Vol. Issue 17, (17) , 1-10
Open AccessInfinite log-convexity
Criteria to verify log-convexity of sequences is presented. Iterating this criteria produces infinitely log-convex sequences. As an application, several classical examples of sequences arising in Combinatorics and Special Functions are presented. The paper concludes with a conjecture regarding coefficients of chromatic polynomials.
- Open Access
- 20 May 2022
- Published by MDPI AG in Mathematics
- Vol. 10 (10) , 1745
Analytic Expressions for Debye Functions and the Heat Capacity of a Solid
Analytic expressions for the N-dimensional Debye function are obtained by the method of brackets. The new expressions are suitable for the study of heat capacity of solids and the analysis of the asymptotic behavior of this function, both in the high and low temperature limits.
- 20 May 2022
- Published by MDPI AG in Mathematics
- Vol. 10 (10) , 1745
Open AccessAnalytic Expressions for Debye Functions and the Heat Capacity of a Solid
Analytic expressions for the N-dimensional Debye function are obtained by the method of brackets. The new expressions are suitable for the study of heat capacity of solids and the analysis of the asymptotic behavior of this function, both in the high and low temperature limits.
- Open Access
- 31 December 2021
- Published by Combinatorial Press in Online Journal of Analytic Combinatorics
- Vol. Issue 16, (16) , 1-21
On the \(r\)-derangements of type BExtensions of a set partition obtained by imposing bounds on the size of the parts and the coloring of some of the elements are examined. Combinatorial properties and the generating functions of some counting sequences associated with these partitions are established. Connections with Riordan arrays are presented.
- 31 December 2021
- Published by Combinatorial Press in Online Journal of Analytic Combinatorics
- Vol. Issue 16, (16) , 1-21
Open AccessOn the \(r\)-derangements of type BExtensions of a set partition obtained by imposing bounds on the size of the parts and the coloring of some of the elements are examined. Combinatorial properties and the generating functions of some counting sequences associated with these partitions are established. Connections with Riordan arrays are presented.
- 28 December 2020
- Published by Elsevier in Journal of Number Theory
- Vol. 223, 325-349
Arithmetic properties of the sum of divisors
- 28 December 2020
- Published by Elsevier in Journal of Number Theory
- Vol. 223, 325-349
Arithmetic properties of the sum of divisors
- Open Access
Filter integrals for orthogonal polynomials
Motivated by an expression by Persson and Strang on an integral involving Legendre polynomials, stating that the square of $P_{2n+1}(x)/x$ integrated over $[-1,1]$ is always $2$, we present analog results for Hermite, Chebyshev, Laguerre and Gegenbauer polynomials as well as the original Legendre polynomial with even index.Open AccessFilter integrals for orthogonal polynomials
Motivated by an expression by Persson and Strang on an integral involving Legendre polynomials, stating that the square of $P_{2n+1}(x)/x$ integrated over $[-1,1]$ is always $2$, we present analog results for Hermite, Chebyshev, Laguerre and Gegenbauer polynomials as well as the original Legendre polynomial with even index. - Open Access
A triple integral analog of a multiple zeta value
We establish the triple integral evaluation \[ \int_{1}^{\infty} \int_{0}^{1} \int_{0}^{1} \frac{dz \, dy \, dx}{x(x+y)(x+y+z)} = \frac{5}{24} \zeta(3), \] as well as the equivalent polylogarithmic double sum \[ \sum_{k=1}^{\infty} \sum_{j=k}^{\infty} \frac{(-1)^{k-1}}{k^{2}} \, \frac{1}{j \, 2^{j}} = \frac{13}{24} \zeta(3). \] This double sum is related to, but less approachable than, similar sums studied by Ramanujan. It is also reminiscent of Euler's formula $\zeta(2,1) = \zeta(3)$, which is the simplest instance of duality of multiple polylogarithms. We review this duality and apply it to derive a companion identity. We also discuss approaches based on computer algebra. All of our approaches ultimately require the introduction of polylogarithms and nontrivial relations between them. It remains an open challenge to relate the triple integral or the double sum to $\zeta(3)$ directly.Open AccessA triple integral analog of a multiple zeta value
We establish the triple integral evaluation \[ \int_{1}^{\infty} \int_{0}^{1} \int_{0}^{1} \frac{dz \, dy \, dx}{x(x+y)(x+y+z)} = \frac{5}{24} \zeta(3), \] as well as the equivalent polylogarithmic double sum \[ \sum_{k=1}^{\infty} \sum_{j=k}^{\infty} \frac{(-1)^{k-1}}{k^{2}} \, \frac{1}{j \, 2^{j}} = \frac{13}{24} \zeta(3). \] This double sum is related to, but less approachable than, similar sums studied by Ramanujan. It is also reminiscent of Euler's formula $\zeta(2,1) = \zeta(3)$, which is the simplest instance of duality of multiple polylogarithms. We review this duality and apply it to derive a companion identity. We also discuss approaches based on computer algebra. All of our approaches ultimately require the introduction of polylogarithms and nontrivial relations between them. It remains an open challenge to relate the triple integral or the double sum to $\zeta(3)$ directly.