Christophe Vignat

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All published works

Action	Title	Year	Authors
+ PDF Chat	Probabilistic aspects of Jacobi theta functions	2024	Paavo Salminen Christophe Vignat
+	Probabilistic aspects of Jacobi theta functions	2023	Paavo Salminen Christophe Vignat
+	Variations and Extensions of Ramanujan's Identity	2021	Christophe Vignat Sarth Chavan Parth Chavan
+	A Triple Integral representation of Catalan's constant	2021	Sarth Chavan Christophe Vignat
+	Evaluation of Multivariate Integrals based on a Duality Identity for the Stieltjes Transform	2021	Sarth Chavan Christophe Vignat
+	Dirichlet Series Under Standard Convolutions: Variations on Ramanujan's Identity for Odd Zeta Values	2021	Parth Chavan Sarth Chavan Christophe Vignat Tanay Wakhare
+	Evaluation of multivariate integrals based on a duality identity for the Stieltjes transform	2021	Sarth Chavan Christophe Vignat
+	Integrals involving Bernoulli and Euler polynomials	2020	Victor H. Moll Christophe Vignat
+	A triple integral analog of a multiple zeta value	2020	Tewodros Amdeberhan Victor H. Moll Armin Straub Christophe Vignat
+	A continuous analogue of lattice path enumeration: Part II	2019	Tanay Wakhare Christophe Vignat
+	Connection Coefficients for Higher-order Bernoulli and Euler Polynomials: A Random Walk Approach	2019	Lin Jiu Christophe Vignat
+	Corrections to “connection Coefficients for Higher-order Bernoulli and Euler Polynomials: A Random Walk Approach”	2019	Lin Jiu Christophe Vignat
+	Taylor coefficients of the Jacobi $\theta_{3}\left( q \right)$ function.	2019	Tanay Wakhare Christophe Vignat
+ PDF Chat	Nonconventional limits of random sequences related to partitions of integers	2019	Jordan Stoyanov Christophe Vignat
+	Non-Conventional Limits of Random Sequences Related to Partitions of Integers	2019	Jordan Stoyanov Christophe Vignat
+ PDF Chat	About some identities for Bessel polynomials	2019	Christophe Vignat
+	Identities for Bernoulli polynomials related to multiple Tornheim zeta functions	2019	Karl Dilcher Armin Straub Christophe Vignat
+	Taylor coefficients of the Jacobi $θ_{3}\left( q \right)$ function	2019	Tanay Wakhare Christophe Vignat
+	Settling some sum suppositions	2018	Tanay Wakhare Christophe Vignat
+	Infinite products involving Dirichlet characters and cyclotomic polynomials	2018	Karl Dilcher Christophe Vignat
+	Simple proofs and expressions for the restricted partition function and its polynomial part	2018	Sinai Robins Christophe Vignat
+ PDF Chat	Woon’s tree and sums over compositions	2018	Christophe Vignat Tanay Wakhare
+	Connection Coefficients for Higher-order Bernoulli and Euler Polynomials: A Random Walk Approach	2018	Lin Jiu Christophe Vignat
+	Structural properties of multiple zeta values	2018	Tanay Wakhare Christophe Vignat
+	Settling some sum suppositions	2018	Tanay Wakhare Christophe Vignat
+	Structural identities for generalized multiple zeta values	2017	Tanay Wakhare Christophe Vignat
+	Woon's tree and sums over compositions	2017	Christophe Vignat Tanay Wakhare
+	A continuous analogue of lattice path enumeration	2017	Tanay Wakhare Christophe Vignat Quang-Nhat Le Sinai Robins
+	Finite generating functions for the sum of digits sequence	2017	Christophe Vignat Tanay Wakhare
+ PDF Chat	A series involving Catalan numbers: Proofs and demonstrations	2016	Tewodros Amdeberhan Xiao Wei Guan Lin Jiu Victor H. Moll Christophe Vignat
+	A base-$b$ extension of the binomial coefficient	2016	Tanay Wakhare Christophe Vignat
+	On the continuous binomial coefficients by L. Cano and R. Diaz	2016	Tanay Wakhare Christophe Vignat
+ PDF Chat	On Binomial Identities in Arbitrary Bases	2016	Lin Jiu Christophe Vignat
+	Base-$b$ analogues of classic combinatorial objects	2016	Tanay Wakhare Christophe Vignat
+	The integrals in Gradshteyn and Ryzhik. Part 29: Chebyshev polynomials	2016	Victor H. Moll Christophe Vignat
+	The integrals in Gradshteyn and Ryzhik. Part 30: Trigonometric functions	2016	Tewodros Amdeberhan Atul Dixit Xiao Wei Guan Li Jiu Alexey Kuznetsov Victor H. Moll Christophe Vignat
+	On Binomial Identities in Arbitrary Bases	2016	Lin Jiu Christophe Vignat
+	A Continuous Analogue of Lattice Path Enumeration: Part II	2016	Tanay Wakhare Christophe Vignat
+ PDF Chat	Generalized Bernoulli Numbers and a Formula of Lucas	2015	Victor H. Moll Christophe Vignat
+	The Zagier polynomials. Part III: Asymptotics and Exact formulas	2015	Atul Dixit M. L. Glasser Victor H. Moll Christophe Vignat
+	A symbolic approach to multiple zeta values at the negative integers	2015	Victor H. Moll Lin Jiu Christophe Vignat
+	Asymptotics and exact formulas for Zagier polynomials	2015	Atul Dixit M. L. Glasser Victor H. Moll Christophe Vignat
+ PDF Chat	THE FINITE FOURIER TRANSFORM OF CLASSICAL POLYNOMIALS	2014	Atul Dixit Lin Jiu Victor H. Moll Christophe Vignat
+ PDF Chat	Identities for generalized Euler polynomials	2014	Lin Jiu Victor H. Moll Christophe Vignat
+	The finite Fourier transform of classical polynomials	2014	Atul Dixit Lin Jiu Victor H. Moll Christophe Vignat
+	Generalized Bernoulli numbers and a formula of Lucas	2014	Victor H. Moll Christophe Vignat
+	Identities for generalized Euler polynomials	2014	Lin Jiu Victor H. Moll Christophe Vignat
+	The finite Fourier transform of classical polynomials	2014	Atul Dixit Lin Jiu Victor H. Moll Christophe Vignat
+	Modified Nörlund polynomials	2014	Atul Dixit Adam Kabza Victor H. Moll Christophe Vignat
+	A probabalistic interpretation of a sequence related to Narayana polynomials	2013	Tewodros Amdeberhan Victor H. Moll Christophe Vignat
+ PDF Chat	Proof of a conjecture by Gazeau <i>et al.</i> using the Gould-Hopper polynomials	2013	Christophe Vignat Olivier Lévêque
+	A probabilistic interpretation of a sequence related to Narayana numbers	2013	Tewodros Amdeberhan Victor H. Moll Christophe Vignat
+	Recursion Rules for the Hypergeometric Zeta Functions	2013	Alyssa Byrnes Lin Jiu Victor H. Moll Christophe Vignat
+ PDF Chat	Proof of a conjecture by Gazeau et al. using the Gould Hopper polynomials	2013	Christophe Vignat Olivier Lévêque
+	A probabilistic interpretation of a sequence related to Narayana polynomials	2012	Tewodros Amdeberhan Victor H. Moll Christophe Vignat
+	A new proof of a Conjecture by D. Zeilberger about Catalan numbers	2012	Tewodros Amdeberhan Victor H. Moll Christophe Vignat
+	Generalized Cramér–Rao relations for non-relativistic quantum systems	2012	J. S. Dehesa A. Plastino P. Sánchez‐Moreno Christophe Vignat
+	A probabilistic interpretation of the Volkenborn integral	2012	Ashwani K. Bhandari Christophe Vignat
+	About some identities for Bessel polynomials	2012	Christophe Vignat
+	Probabilistic proofs of some relationships between the Bernoulli and Euler polynomials	2012	H. M. Srivastava Christophe Vignat
+	A probabilistic approach of sum rules for heat polynomials	2011	Olivier Lévêque Christophe Vignat
+	A probabilistic approach to some binomial identities	2011	Christophe Vignat Victor H. Moll
+ PDF Chat	Quantum potentials with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si27.gif" display="inline" overflow="scroll"><mml:mi>q</mml:mi></mml:math>-Gaussian ground states	2011	Christophe Vignat A. Plastino A. Plastino J. S. Dehesa
+ PDF Chat	A generalized Isserlis theorem for location mixtures of Gaussian random vectors	2011	Christophe Vignat
+ PDF Chat	Old and new results about relativistic Hermite polynomials	2011	Christophe Vignat
+ PDF Chat	Derivation of an integral of Boros and Moll via convolution of Student t-densities	2011	Christian Berg Christophe Vignat
+ PDF Chat	Entropic upper bound on gravitational binding energy	2011	Christophe Vignat A. Plastino A. Plastino
+	Lower bounds on Information Divergence	2011	Peter Harremoës Christophe Vignat
+	A generalized Isserlis theorem for location mixtures of Gaussian random vectors	2011	Christophe Vignat
+	A probabilistic approach to some binomial identities	2011	Christophe Vignat Victor H. Moll
+ PDF Chat	A probabilistic approach to some results by Nieto and Truax	2010	Christophe Vignat
+ PDF Chat	On a conjecture about Dirac’s delta representation using q-exponentials	2010	Antoine Chevreuil A. Plastino Christophe Vignat
+ PDF Chat	Diversity-Multiplexing Tradeoff for the MIMO Static Half-Duplex Relay	2010	Olivier Lévêque Christophe Vignat Melda Yüksel
+	Generalized Cramer-Rao relations for non-relativistic quantum systems	2010	J. S. Dehesa Angelo Plastino P. Sánchez‐Moreno Christophe Vignat
+	Quantum Potentials with q-Gaussian Ground States	2010	Christophe Vignat Angelo Plastino Angelo Plastino J. S. Dehesa
+	An H-theorem for the Brownian motion on the hyperbolic plane	2010	Christophe Vignat Pedro W. Lamberti
+ PDF Chat	On a conjecture about Dirac's delta representation using q-Gaussians	2010	Antoine Chevreuil Angelo Plastino Christophe Vignat
+	Estimation MAP pour des variables elliptiquement distribuées	2009	Steeve Zozor Christophe Vignat
+	On the MAP estimation in the context of elliptical distributions	2009	Steeve Zozor Christophe Vignat
+	On minimum Fisher information distributions with restricted support and fixed variance	2009	Jean‐François Bercher Christophe Vignat
+ PDF Chat	Geometric aspects of the non-extensive statistical theory	2009	Christophe Vignat Jean‐François Bercher Paul M. Goggans Chun-Yong Chan
+	On the density of the sum of two independent Student t-random vectors	2009	Christian Berg Christophe Vignat
+	Some entropic extensions of the uncertainty principle	2008	Steeve Zozor M. Portesi Christophe Vignat
+ PDF Chat	An entropic view of Pickands&#x2019; theorem	2008	Jean‐François Bercher Christophe Vignat
+ PDF Chat	On some results of Cufaro Petroni about Student t-processes	2008	Christian Berg Christophe Vignat
+ PDF Chat	Some extensions of the uncertainty principle	2008	Steeve Zozor M. Portesi Christophe Vignat
+ PDF Chat	An extension of Wick’s theorem	2008	Christophe Vignat Shalabh Bhatnagar
+	An entropic view of Pickands' theorem	2008	Jean‐François Bercher Christophe Vignat
+	Central limit theorem and deformed exponentials	2007	Christophe Vignat Angelo Plastino
+	Forme entropique du principe d'incertitude et cas d'égalité asymptotique	2007	Steeve Zozor Christophe Vignat
+ PDF Chat	Scale invariance and related properties of q-Gaussian systems	2007	Christophe Vignat A. Plastino
+ PDF Chat	Some results concerning maximum Rényi entropy distributions	2007	Oliver Johnson Christophe Vignat
+	Central limit theorem, deformed exponentials and superstatistics	2007	Christophe Vignat A. Plastino
+	An extension of Wick's theorem	2007	Christophe Vignat Shalabh Bhatnagar
+ PDF Chat	Power-law random walks	2006	Christophe Vignat A. Plastino
+ PDF Chat	Linearization Coefficients of Bessel Polynomials and Properties of Student t-Distributions	2006	Christian Berg Christophe Vignat
+ PDF Chat	Estimation in a fluctuating medium and power-law distributions	2006	Christophe Vignat Ángel Luis Plastino
+	Elliptical invariance of distributions of the power type: t he stability and extensivity issues	2006	Christophe Vignat A. Plastino
+ PDF Chat	A note on bounded entropies	2006	Pierre‐Olivier Amblard Christophe Vignat
+ PDF Chat	Correlated Gaussian systems exhibiting additive power-law entropies	2006	Christophe Vignat A. Plastino A. Plastino
+ PDF Chat	Poincare's Observation and the Origin of Tsallis Generalized Canonical Distributions	2006	Angelo Plastino Christophe Vignat
+	Elliptical invariance of distributions of the power type: the stability and extensivity issues	2006	Christophe Vignat A. Plastino
+ PDF Chat	Density operators that extremize Tsallis entropy and thermal stability effects	2005	Christophe Vignat A. Plastino
+	Linearization coefficients of Bessel polynomials	2005	Christian Berg Christophe Vignat
+	Geometric origin of probabilistic distributions in statistical mechanics	2005	Christophe Vignat A. Plastino
+	Superstatistics Based on the Microcanonical Ensemble	2005	Christophe Vignat A. Plastino Angelo Plastino
+	Stochastic invertible mappings between power law and Gaussian probability distributions	2005	Christophe Vignat A. Plastino
+ PDF Chat	The p-sphere and the geometric substratum of power law probability distributions	2005	Christophe Vignat Angelo Plastino
+ PDF Chat	Stability of families of probability distributions under reduction of the number of degrees of freedom	2004	Christophe Vignat Jan Naudts
+	About closedness by convolution of the Tsallis maximizers	2004	Christophe Vignat
+	About closedness by convolution of the Tsallis maximizers	2004	Christophe Vignat Alfred O. Hero Jose A. Costa
+	Matrix Fisher inequalities for non-invertible linear systems	2003	Christophe Vignat Jean‐François Bercher
+ PDF Chat	On Solutions to Multivariate Maximum α-Entropy Problems	2003	Jose A. Costa Alfred O. Hero Christophe Vignat
+ PDF Chat	A Nash Equilibrium related to the Poisson Channel	2003	Peter Harremoës Christophe Vignat
+	An Entropy Power Inequality for the binomial family	2003	Peter Harremoës Christophe Vignat
+	A Characterization of the Multivariate Distributions Maximizing	2002	Josk A. Costa Christophe Vignat UniversitB de Marne-la-VallBe Enst Ura

Common Coauthors

Coauthor	Papers Together
Victor H. Moll	22
Tanay Wakhare	16
Lin Jiu	13
A. Plastino	10
Atul Dixit	7
Tewodros Amdeberhan	7
Angelo Plastino	7
Steeve Zozor	5
Christian Berg	5
Jean‐François Bercher	5
Sarth Chavan	5
J. S. Dehesa	4
A. Plastino	4
Olivier Lévêque	4
Peter Harremoës	3
Jose A. Costa	2
Armin Straub	2
Parth Chavan	2
Xiao Wei Guan	2
M. L. Glasser	2
Antoine Chevreuil	2
Karl Dilcher	2
Shalabh Bhatnagar	2
Jordan Stoyanov	2
Sinai Robins	2
Paavo Salminen	2
P. Sánchez‐Moreno	2
Alfred O. Hero	2
M. Portesi	2
Melda Yüksel	1
Pierre‐Olivier Amblard	1
Li Jiu	1
Adam Kabza	1
Alexey Kuznetsov	1
Pedro W. Lamberti	1
H. M. Srivástava	1
Jan Naudts	1
Enst Ura	1
Ashwani K. Bhandari	1
Paul M. Goggans	1
UniversitB de Marne-la-VallBe	1
Josk A. Costa	1
Quang-Nhat Le	1
Ángel Luis Plastino	1
Chun-Yong Chan	1
Victor H. Moll	1
Oliver Johnson	1
Alyssa Byrnes	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Table of Integrals, Series, and Products	1980		12
+	About closedness by convolution of the Tsallis maximizers	2004	Christophe Vignat Alfred O. Hero Jose A. Costa	7
+	A Treatise on the Theory of Bessel Functions.	1923	Matthew Porter G. N. Watson	5
+ PDF Chat	Superstatistics	2003	Christian Beck E. G. D. Cohen	5
+ PDF Chat	The p-sphere and the geometric substratum of power-law probability distributions	2005	C. Vignat A. Plastino	4
+ PDF Chat	Poincaré's observation and the origin of Tsallis generalized canonical distributions	2006	C. Vignat A. Plastino	4
+ PDF Chat	Fingerprints of nonextensive thermodynamics in a long-range Hamiltonian system	2002	Vito Latora Andrea Rapisarda Constantino Tsallis	4
+ PDF Chat	Dynamical Foundations of Nonextensive Statistical Mechanics	2001	Christian Beck	4
+ PDF Chat	On a Class of Distributions Stable Under Random Summation	2012	Lev B. Klebanov A. V. Kakosyan Svetlozar T. Rachev Grigory Temnov	4
+	Sums of Products of Bernoulli Numbers	1996	Karl Dilcher	4
+ PDF Chat	Applications of the classical umbral calculus	2003	Ira M. Gessel	4
+	Symmetric Multivariate and Related Distributions.	1991	Sanat K. Sarkar Kai-Tai Fang Samuel Kotz Kai-Wang Ng	4
+	Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables	1965	D. B. Owen Milton Abramowitz Irene A. Stegun	4
+ PDF Chat	The Zagier modification of Bernoulli numbers and a polynomial extension. Part I	2013	Atul Dixit Victor H. Moll Christophe Vignat	4
+	Stellar polytropes and Tsallis' entropy	1993	A. Plastino A. Plastino	3
+ PDF Chat	Renormalization group approach to nonextensive statistical mechanics	2001	R. S. Mendes Constantino Tsallis	3
+	Information theoretic inequalities	1991	Amir Dembo Thomas M. Cover J. Thomas	3
+	The Umbral Calculus	1984	Steven Roman	3
+	The Distribution of Linear Combinations of<i>t</i>-Variables	1978	Glenn A. Walker John G. Saw	3
+ PDF Chat	The student t-distribution of any degree of freedom is infinitely divisible	1976	Emil Grosswald	3
+	Moment representation of Bernoulli polynomial, Euler polynomial and Gegenbauer polynomials	2007	Ping Sun	3
+ PDF Chat	Entropy and the Central Limit Theorem	1986	Andrew R. Barron	3
+	A generalization of the digital binomial theorem	2015	Hiêú D. Nguyêñ	3
+ PDF Chat	Superstatistics, escort distributions, and applications	2004	Christian Beck	3
+ PDF Chat	Superstatistical generalization of the work fluctuation theorem	2004	Christian Beck E. G. D. Cohen	3
+ PDF Chat	On classes of non-Gaussian asymptotic minimizers in entropic uncertainty principles	2006	Steeve Zozor C. Vignat	3
+ PDF Chat	On Solutions to Multivariate Maximum α-Entropy Problems	2003	Jose A. Costa Alfred O. Hero Christophe Vignat	3
+ PDF Chat	Two integer sequences related to Catalan numbers	2012	Michel Lassalle	3
+	A Digital Binomial Theorem	2014	Hiêú D. Nguyêñ	3
+	Introduction to Nonextensive Statistical Mechanics	2009	Constantino Tsallis	3
+ PDF Chat	Density operators that extremize Tsallis entropy and thermal stability effects	2005	Christophe Vignat A. Plastino	3
+ PDF Chat	Formulation of the uncertainty relations in terms of the Rényi entropies	2006	Iwo Białynicki‐Birula	3
+ PDF Chat	Superstatistics in hydrodynamic turbulence	2004	Christian Beck	3
+ PDF Chat	Asymptotics of superstatistics	2005	Hugo Touchette Christian Beck	3
+	A General Class of Coefficients of Divergence of One Distribution from Another	1966	Syed Mustafa Ali S. D. Silvey	2
+	Special Functions: An Introduction to the Classical Functions of Mathematical Physics	1997	Nico Μ. Τemme Daniel Zwillinger	2
+	Methods of Modern Mathematical Physics	1972	Michael C. Reed Barry Simon	2
+ PDF Chat	On a class of random variables	1955	Frank Spitzer	2
+	Cramer–Rao information plane of orthogonal hypergeometric polynomials	2005	J. S. Dehesa P. Sánchez‐Moreno R. J. Yáñez	2
+	The Gaussian Transform of Distributions: Definition, Computation and Application	2006	Teodor Alecu Slava Voloshynovskiy Thierry Pun	2
+	Ramanujan’s Notebooks: Part V	1997	Bruce C. Berndt	2
+	The role of constraints within generalized nonextensive statistics	1998	Constantino Tsallis RenioS. Mendes A. Plastino	2
+ PDF Chat	Arbitrary-order Hermite generating functions for obtaining arbitrary-order coherent and squeezed states	1995	Michael Martin Nieto D. Rodney Truax	2
+ PDF Chat	Generalized thermostatistics based on deformed exponential and logarithmic functions	2004	Jan Naudts	2
+ PDF Chat	Residual Life Time at Great Age	1974	A. A. Balkema Laurens de Haan	2
+	The Special Functions and Their Approximations	1972	C. W. Clenshaw Yudell L. Luke	2
+	Student's t- and r-distributions: Unified derivation from an entropic variational principle	1997	André M. C. Souza Constantino Tsallis	2
+	A Recursive Formulation of the Old Problem of Obtaining Moments from Cumulants and Vice Versa	1995	Peter J. Smith	2
+ PDF Chat	Inequalities in Fourier Analysis on <i> R <sup>n</sup> </i>	1975	William Beckner	2
+	Empirical Process Techniques for Dependent Data	2002	Herold Dehling Walter Philipp	2