K. Dilcher and C. Vignat, An explicit form of the polynomial part of a restricted partition function, Research in Number Theory, 3:1, 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, 84, 1-13, 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, to appear, Elemente der Mathematik, 67, 1-8, 2012
C. Vignat, A generalized Isserlis theorem for location mixtures of Gaussian random vectors, Statistics and Probability Letters, 82-1, 67-71, Jan. 2012
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
C. Vignat, Old and New results about Relativistic Hermite polynomials, J. Math. Phys. 52, 093503, 2011
C. Vignat and P.W. Lamberti, H theorems for the Brownian motion on the hyperbolic plane, Physica A: Statistical Mechanics and its Applications 391, 544-551, 2012
C. Vignat, A. Plastino, A.R. Plastino and J.S. Dehesa, Quantum Potentials with q-Gaussian Ground States, Physica A, 391, 1068-1073, 2012
C. Vignat, A. Plastino and A.R. Plastino, Entropic Upper Bound on Gravitational Binding Energy, Physica A: Statistical Mechanics and Applications, 390, 13, 2491-2496, July 2011
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
S.Zozor and C. Vignat, Spectral measure of the harmonic oscillator with alpha-stable noise, Phys. Rev. E 84, 031115, 2011
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
C. Berg and C. Vignat, Derivation of an integral of Boros and Moll via convolution of Student t-densities, Ramanujan Journal, 27-2, 147-150, 2012
A. Chevreuil, A. Plastino and C. Vignat, On a conjecture about Dirac's delta representation using q-exponentials, J. Math. Phys. 51, 093502, 2010
O. Leveque, C. Vignat and M. Yuksel, Diversity-Multiplexing Tradeoff for the MIMO Static Half-Duplex Relay, IEEE Tr. on Information Theory, 56-7, 3356 - 3368, July 2010
C. Vignat, A probabilistic approach to some results by Nieto and Truax, J. Math. Phys. 51, 2010, 123505
C. Berg and C. Vignat, On the density of the sum of two independent Student t-random vectors, Statistics and Probability Letters 80, 13-14, 2010, 1043-1055
S. Zozor and C. Vignat, Some Results on the Denoising Problem in the Elliptically Distributed Context, IEEE Transactions on Signal Processing, 58-1, 2010, 134-150
C. Vignat and A. Plastino Why is the detection of q-Gaussian behavior such a common occurrence? , Physica A, Volume 388-5, 2009, 601-608
F. Pennini, A. Plastino, B.H. Soffer and C. Vignat, Physical symmetries and Fisher's information measure, Physics Letters A, Volume 373, Issues 8-9, 2009, 817-820
C. Vignat and A. Plastino, Geometry of the central limit theorem in the nonextensive case, Physics Letters A Volume 373, Issue 20, 2009, 1713-1718
C. Vignat and P.W. Lamberti, A study of the orthogonal polynomials associated with the quantum harmonic oscillator on constant curvature spaces, J. Math. Phys. 50, 103514, 2009
J.-F. Bercher and C. Vignat, On minimum Fisher information distributions with restricted support and fixed variance, Information Sciences, 179-22, November 2009, 3832-3842
C. Berg and C. Vignat, Linearization Coefficients of Bessel Polynomials and Properties of Student t-Distributions, Constructive Approximation, Vol. 27, 2008, 15-32
C. Berg and C. Vignat, On some results of Cufaro Petroni about Student t-processes, J. Phys. A: Math. Theor. 41, 2008, 265004
S. Zozor, M. Portesi and C. Vignat, Some extensions of the uncertainty principle, Physica A, Volume 387, Issues 19-20, 2008, 4800-4808
J.-F. Bercher and C. Vignat, A new look at q-exponential distributions via excess statistics, Physica A, Volume 387, Issue 22, 15 September 2008, 5422-5432
C. Vignat and S. Bhatnagar, An extension of Wick's theorem, Statistics & Probability Letters, Volume 78, Issue 15, 2008, 2404-2407
O. Johnson and C. Vignat, Some results concerning maximum Rényi entropy distributions, Annales de l'Institut Henri Poincaré (B) Probability and Statistics, Vol 43-3, 2007, 339-351
C. Vignat and A. Plastino, Estimation in a fluctuating medium and power-law distributions, Phys. Lett. A 360, 2007 , 415-418
C. Vignat and A. Plastino, Scale invariance and related properties of q-Gaussian systems, Physics Letters A, Volume 365, 5-6, 2007, 370-375
C. Vignat and A. Plastino, Central limit theorem and deformed exponentials , J. Phys. A: Math. Theor. 40(45), 2007, F969-F978
C. Vignat and A. Plastino, Power-law random walks, Phys. Rev. E 74, 2006 , 051124
C. Vignat and A. Plastino, Density operators that extremize Tsallis entropy and thermal stability effects, , Physica A, Volume 361-1, 2006, 139-160
C. Vignat and A. Plastino, Stochastic invertible mappings for Tsallis distributions, Comptes Rendus Physique Volume 7, Issues 3-4 , April-May 2006, 442-448
C. Vignat, A. Plastino and A.R. Plastino, Correlated Gaussian Systems exhibiting additive Power-Law Entropies, Physics Letters A, Volume 354, Issues 1-2, 2006, Pages 27-30
C. Vignat, A. Plastino and A.R. Plastino, Superstatistics based on the microcanonical ensemble, Nuovo Cimento B, vol. 120 B n.9, 2005, pp 951-963
C. Vignat and A. Plastino, The p-sphere and the geometric substratum of power law probability distributions, Physics Letters A, Volume 343, Issue 6, 2005, pp 411-416
F. Sagnard, F. Bentabet, C. Vignat, In Situ Measurements of the Complex Permittivity of Materials Using Reflection Ellipsometry in the Microwave Band: Theory (Part I), IEEE Tr. Instr. and Measurements, Volume 54, Issue 3, June 2005, 1266 - 1273
F. Sagnard, F. Bentabet, C. Vignat, In Situ Measurements of the Complex Permittivity of Materials Using Reflection Ellipsometry in the Microwave Band: Experiments (Part II), IEEE Tr. Instr. and Measurements, Volume 54, Issue 3, June 2005, 1274 - 1282
F. Sagnard, C. Vignat, Extension of the analytical modelling of resistive loaded thin-wire antennas to Gaussian derivatives excitations, Microwave and Optical Technology Letters, vol 47-6, 548-553, Dec. 2005
C. Vignat and J. Naudts, Stability of families of probability distributions under reduction of the number of degrees of freedom, Physica A, Volume 350, 2-4 , 15 May 2005, 296-302
C. Vignat and J.-F. Bercher, On Fisher Information Inequalities and Score Functions in non-invertible Linear Systems, JIPAM, Volume 4, Issue 4, 2003, Article 71
C. Vignat and J.-F. Bercher, Analysis of signals in the Fisher-Shannon information plane, Physics Letters A 312, 2003, 27–33
P. Harremoës and C. Vignat, A Nash Equilibrium related to the Poisson Channel, Communications in Information and Systems, vol. 3-3, pp. 183-190 , 2003
P. Harremoës and C. Vignat, An Entropy Power Inequality for the binomial family, Journal of Inequalities in Pure and Applied Mathematics, Volume 4, Issue 5, 2003, Article 93
J.-F. Bercher, C. Vignat, Estimating the entropy of a signal with applications, IEEE Trans. on Signal Processing, vol. 48, n.6, June 2000, pp.1687-94.
F. Sagnard, F. Bentabet, C. Vignat, Theoretical Study of Methods based on Ellipsometry for measurement of complex Permittivity of Materials, Electronic Letters, 26th October 2000, no 22, pp.1843-45
A. Chevreuil, F. Desbouvries, A. Gorokhov, P. Loubaton and C. Vignat, Blind equalization in the presence of jammers and unknown noise, IEEE Trans. on Signal Processing. Vol 46 no 1, pages 259-263, January 1998.
G. Dreyfus, O. Macchi, S. Marcos, L. Personnaz, P. Roussel-Ragot, C. Vignat, Réseaux de neurones pour le filtrage non-linéaire adaptatif, Traitement du Signal, Fév 92
S. Marcos, O. Macchi, C. Vignat, G. Dreyfus, L. Personnaz, P. Roussel-Ragot, A Unified Framework for Gradient Algorithms Used for Filter Adaptation and Neural Network Training, International Journal of Circuit Theory and Applications, vol. 20,pp. 159- 200, 1992,
International Journal of Circuit Theory and Applications Best Paper Award 1992