RECENT PAPERS

T. Wakhare and C. Vignat, Structural properties of multiple zeta values, submitted to Research in Number Theory

L. Jiu and C. Vignat, Connection coefficients for higher-order Bernoulli and Euler polynomials: a random walk approach, submitted to Fibonnacci Quarterly

T. Wakhare and C. Vignat, Settling some sums suppositions, to appear, Acta Arithmetica Hungarica

S. Robins and C. Vignat, Simple proofs and expressions for the restricted partition function and its polynomial part, submitted

K. Dilcher and C. Vignat, Infinite products involving Dirichlet characters and cyclotomic polynomials, Advances in Applied Mathematics, 100, 43-70, 2018

T. Wakhare and C. Vignat, A continuous analog of lattice path enumeration, part II, submitted, Online Journal of Analytic Combinatorics

C. Vignat and T. Wakhare, Finite generating functions for the sum-of-digits sequence, to appear, Ramanujan Journal

T. Wakhare and C. Vignat, Multiple Zeta values for classical special functions, submitted, Ramanujan Journal

C. Vignat and T.V. Wakhare, Woon’s tree and sums over compositions, Journal of Integer Sequences, 21, 18.3.4, 2018

T.V. Wakhare and C. Vignat, Base-$b$ analogues of classic combinatorial objects, submitted to Minnesota Journal of Undergraduate Mathematics

T. Wakhare, C. Vignat, Q.-N. Le and S. Robins, A continuous analogue of lattice path enumeration, submitted

K. Dilcher and C. Vignat, An explicit form of the polynomial part of a restricted partition function, Research in Number Theory, 3:1, 1-12, 2017

“Dedicated to the memory of our friend and colleague Jonathan M. Borwein, mathematician extraordinaire”

L. Jiu and C. Vignat, On binomial identities in arbitrary bases, Journal of Integer Sequences, vol 19, 16.5.5, 2016

V. De Angelis and C. Vignat, Euler Polynomials and Identities for Non-Commutative Operators, Journal of Mathematical Physics, 56, 123506, 2015

K. Dilcher and C. Vignat, General convolutions identities for Bernoulli and Euler polynomials, Journal of Mathematical Analysis and Applications, 435-2, 1478-1498, March 2016

A. Dixit, M. L. Glasser, V. H. Moll and C. Vignat, Asymptotics and exact formulas for Zagier polynomials, Research in Number Theory, 2:12, 2016

L. Jiu, V. H. Moll and C. Vignat, A symbolic approach to some identities for Bernoulli-Barnes polynomials, International Journal of Number Theory, 12-3, 649-662, 2016

T. Amdeberhan, X. Guan, L. Jiu, V. H. Moll and C. Vignat, A series involving Catalan numbers. Proofs and demonstrations, Elemente der Mathematik, 71-3, 109-121, 2016

V. H. Moll, L. Jiu and C. Vignat, A symbolic approach to multiple zeta values at the negative integers, Journal of Symbolic Computation, Volume 84, 1-13, January-February 2018

V. H. Moll and C. Vignat, The integrals in Gradshteyn and Ryzhik. Part 29: Chebyshev polynomials, Scientia, 27, 2016, 31-40

V. H. Moll, T. Amdeberhan, A. Dixit, X. Guan, L. Jiu, A. Kuznetsov and C. Vignat, The integrals in Gradshteyn and Ryzhik. Part 30: Trigonometric functions, Scientia, 27, 2016, 47-74

J.M. Borwein, A. Straub and C. Vignat, Densities of short uniform random walks in higher dimensions, Journal of Mathematical Analysis and Applications, 437-1, 668-707, May 2016

A. Dixit, A. Kabza, V.H. Moll and C. Vignat, Modified Nörlund Polynomials, Ramanujan Journal, 42-1, January 2017, 69-96

K. Dilcher and C. Vignat, Euler and the strong law of small numbers, The American Mathematical Monthly, 123, 5, 486-490, 2016

V. H. Moll and C. Vignat, Solutions to the Monthly problems 11739, 11765 and 11791

A. Dixit, L. Jiu, V. H. Moll and C. Vignat, The finite Fourier transform of classical polynomials, Journal of the Australian Mathematical Society, 98, 145-160, 2015

V. H Moll and C. Vignat, Generalized Bernoulli numbers and a formula of Lucas, Fibonacci Quarterly, 53-4, 349, 2015

L. Jiu, V. H. Moll and C. Vignat, Identities for Generalized Euler Polynomials, Journal of Integral Transforms and Special Functions, 25-10, 777-789, 2014

A.R. Plastino, C. Vignat and A. Plastino, Variational Principle for a Schrödinger Equation with non-Hermitian Hamiltonian and Position-Dependent Mass, Communications in Theoretical Physics, 63-3, 275-278, 2015

V. H. Moll and C. Vignat, On polynomials connected to powers of Bessel functions, International Journal of Number Theory, 10-5, 1245-1257, 2014

A. Byrnes, L. Jiu, V. H. Moll and C. Vignat, Recursion Rules for the Hypergeometric Zeta Functions, International Journal of Number Theory, vol. 10, No 7, 1761-1782, 2014

C. Vignat and O. Leveque, Proof of a conjecture by Gazeau et al. using the Gould Hopper polynomials, J. Math. Phys. 54, 073513, 2013

T. Amdeberhan, V. de Angelis, A. Dixit, V. H. Moll and C. Vignat, From sequences to polynomials and back, Journal of Mathematical Physics 54, 123502, 2013

O. Leveque and C. Vignat, About some identities for Bessel polynomials, submitted, Integral Transforms and Special Functions

A. Dixit, V. H. Moll and C. Vignat, The Zagier modification of Bernoulli numbers and a polynomial extension. Part I, The Ramanujan Journal, 33-3, 379-422, April 2014

M. W. Coffey, V. de Angelis, A. Dixit, V. H. Moll, A. Straub and C. Vignat, The Zagier polynomials. Part II: Arithmetic Properties of Coefficients, The Ramanujan Journal, 35-3, 361-390, 2014

T. Amdeberhan, V. H. Moll and C. Vignat, A probabilistic interpretation of a sequence related to Narayana numbers, Online Journal of Analytic Combinatorics, Vol. 8, 2013

A. Bhandari and C. Vignat, A probabilistic interpretation of the Volkenborn integral, submitted, Applied Mathematics and Computation

H.M. Srivastava and C. Vignat, Probabilistic proofs of some relationships between the Bernoulli and Euler polynomials, European Journal of Pure and Applied Mathematics, 5-2, 97-107, 2012

C. Vignat and V.H. Moll, A probabilistic approach to some binomial identities, Elemente der Mathematik, 70-2, 55-66, 2015

O. Lévêque, C. Vignat, A probabilistic approach of sum rules for heat polynomials, J. Phys. A: Math. Theor. 45, 015001, 2012

C. Vignat, Moment representations of Bernoulli, Euler and Carlitz Hermite polynomials, submitted, Integral Transforms and Special Functions

T. Amdeberhan, V. H. Moll and C. Vignat, The Evaluation of a Quartic Integral via Schwinger, Schur and Bessel, Ramanujan Journal, 28, 1-14, 2012

J.S. Dehesa, A.R. Plastino, P. Sanchez-Moreno and C. Vignat, Generalized Cramér-Rao relations for non-relativistic quantum systems, Applied Mathematics Letters, 25, 1689-1694, 2012