(with R Barman, A Singh)
Recursive formulas for MacMahon and Ramanujan q-series, preprint.
(with R Barman, A Singh)
Recursive formulas for MacMahon and Ramanujan q-series, preprint.
(with K Ono, M Griffin, A Singh)
Traces of partition Eisenstein series, preprint.
(with G E Andrews, R Tauraso)
Further study on MacMahon-type sums of divisors, accepted: Research in Number Theory.
(with K Ono, A Singh)
Derivatives of theta functions as traces of partition Eisenstein series, accepted: Nagoya Mathematical Journal.
(with R Tauraso)
Congruences for sums of MacMahon's q-Catalan polynomials,
Bulletin Australian Math. Soc.
(firstview) Oct. (2024)
(with J A Sellers, A Singh)
Arithmetic properties for generalized cubic partitions, Aequationes Mathematicae, (online 1st), 10 Sept. (2024).
(with K Ono, A Singh)
MacMahon's sums-of-divisors and allied q-series, Advances in Mathematics, Vol. 452 (2024).
(with S Wagner)
The MacMahon q-Catalan is convex, Annals of Combinatorics,
Vol. 28 (2024).
(with G E Andrews, K Ono, A Singh)
Hook lengths in self-conjugate partitions, Proc. Amer. Math. Soc. Vol. 11 (2024).
(with G E Andrews, R Tauraso)
Extensions of MacMahon's sums of divisors, Research in the Math. Sciences
V. 11, #8 (2024).
(with D Callan)
Gaussian inequality, Rocky Mountain J. Math., V. 54, #6 (2024).
(with G Comert, N Begashaw, N G. Medhin, M Chowdhury)
Estimating the queue lengths from probe vehicles at traffic signals,
Expert Systems with Appl.,
V. 252, Part A (2024).
(with V H Moll, J L Santander, K Mclaughlin, C Koutschan)
Collisionless shock region of the KdV equation, Physica D: Nonlinear Phenomena, 456 (2023).
(with C Koutschan, D Zeilberger)
Yay for determinants!
A revised version appeared, with a different title in
Séminaire Lotharingien de Combinatoire, B89a (2023).
(with W Marszalek)
SIB in multiple transonic crossings of unsteady gravitational flows,
Physics Letters A, V. 477 (2023).
(with G E Andrews, C Ballantine)
Hook length and symplectic content in partitions,
J. Combinatorial Theory, Series A 200 (2023).
(with V H Moll)
Infinite logconvexity, Online Journal of Analytic Combinatorics, V. 17 (2022).
(with G E Andrews, C Ballantine)
Refinements of Beck-type partition identities,
Discrete Math. 345, no. 12, Paper No. 113110, (2022).
(with D Zeilberger)
An elegant Multi-Integral that implies an identity of Dougherty and McCammond.
Palestine J. of Mathematics, Vol. 11 #4 (2022).
(with A Duncan, V H Moll, V Sharma)
Filter integrals for orthogonal polynomials,
Hardy-Ramanujan Journal 44 (2021), 116-135.
(with V H Moll, V Sharma, D Villamizar)
Arithmetic properties of the sum of divisors, J. Number Theory, Vol. 223, June 2021, Pages 325-349.
(with V H Moll, A Straub, C Vignat)
A triple integral analog of a multiple zeta value, International J Number Theory, Vol. 17, No. 02, pp. 223-237 (2021).
(with M Glasser, M Jones, V Moll, R Posey, D Varela)
The Cauchy-Schlomilch transformation, Integral Transforms Spec. Funct. 30 (2019), no. 12, 940-961.
(with R Tauraso)
A congruence for a double harmonic sum,
Scientia, Ser. A, Math. Sci. (N.S.) 29, 37-44 (2019).
(with D Callan, H Ohtsuka and R Tauraso)
Revitalized automatic proofs: demonstrations,
INTEGERS, 17 (2017), Axx.
(with R Tauraso)
Two Triple binomial sum supercongruences (including abelian squares)
Journal of Number Theory, 175 (2017), 140-157.
(with X Guan, L Jiu, V H Moll and C Vignat)
A series involving Catalan numbers:
Proofs and demonstrations,
Elemente der Mathematik, V 71, 2016.
(with R Tauraso)
Supercongruences for the Almkvist-Zudilin numbers,
Acta Arithmetica, 11 May 2016 (online).
Explicit computations with the Divided Symmetrization operator,
Proc. Amer. Math. Soc., V 144, #7, 2016.
(with W Marszalek)
Memristive Jounce (Newtonian) Circuits,
J Applied Mathematical Modelling, V 40, #4, 2016.
(with W Marszalek)
Least action principle for mem-elements,
J circuits, systems & computers, V 24, #10, 2015.
(with E Leven)
Multi-cores, posets, and lattice paths,
Advances in Appl. Math., Vol 71, 2015, pp 1-13.
(with V Moll)
Involutions and their progenies,
J of Combinatorics, Vol 6, #4, 2015.
(with M B Can, M Jensen)
Divisors and specializations of Lucas polynomials,
J of Combinatorics, Vol 6, #1-2, 2015.
(with X Chen, V Moll, B Sagan)
Generalized Fibonacci polynomials and Fibonomial coefficients,
Annals of Combinatorics, V 18, 2014, pp 541-562.
(with A Dixit, X Guan, L Jiu, V Moll)
Unimodality of polynomials from rational integral: proof revisited,
J Math Anal & Appl., V 420, 2014, pp 1154-1166.
(with V. De Angelis, A. Dixit, V Moll, C. Vignat)
From sequences to polynomials via operator orderings,
J. Mathematical Physics, V 54, 2013.
(with D Callan, V H Moll)
p-adic analysis and combinatorics of truncated exponential sums,
J INTEGERS, Vol 13, paper A21, 2013.
(with V H Moll, C Vignat)
A probabilistic interpretation of a sequence related to Narayana
polynomials,
OnLine J Combinatorics, V 8, #3, 2013.
(with D Borwein, J Borwein, A Straub)
Normalizing factor in a q-Dirac delta,
J Mathematical Physics, V.53, #7, 2012.
(with V H Moll, V G Papanicolaou)
A family of palindromic polynomials,
Scientia, Series A: Math. Sciences 24, 2013, pp. 25-32.
(with O Espinosa, I Gonzalez, M Harrison, V H Moll, A Straub)
On Ramanujan's Master Theorem,
(online 1st) The Ramanujan J, 11 Jan. 2012.
(with V De Angelis, V H Moll)
Complementary Bell numbers: Wilf's conjecture,
Advances in Combinatorics, 2013, pp 23-56
Differential operators, shifted parts, and hook lengths,
The Ramanujan J, Vol 24, #3, 2011. Follow the
link for background material.
(with M Can, V H Moll)
Broken bracelets, Molien series, paraffin wax and an elliptic curve of conductor 48,
SIAM J. Discrete Math. V.25, #4, 2011, pp.1843-1859. (warning: large file).
(V de Angelis, M Lin, V H Moll, B Sury)
A binomial identity, Elemente der Mathematik, V.67, #1, 2012,
pp.18-25.
(with V H Moll, C Vignat)
A quartic integral a la Schwinger, Schur and Bessel,
The Ramanujan J, V.28, #1, 2012.
(with V H Moll)
Arithmetic properties of plane partitions in a hypercube,
Elec. J. Combin., V.18, #R1, 2011.
(with C Koutschan, V H Moll, E Rowland)
The iterated integrals of ln(1+x^n),
Inter. J. Number Theory, V.8, #1, 2012.
(with V H Moll)
A by-product of an integral evaluation,
The Ramanujan J, V 37, 2015, pp 219-222.
(with L Medina, V Moll)
Gems in Experimental Mathematics, this book is V.517, AMS
Contemporary Math, July 2010.
(with Coffey, Espinosa, Koutschan, Manna, Moll)
Integrals of powers of loggamma,
Proc. Amer. Math. Soc., #139, 2011.
(with O Espinosa, V Moll, A Straub)
Wallis-Ramanujan-Schur-Feynman,
Amer. Math. Monthly, August/Sept., 2010.
A note on a question due to A. Garsia, , in
Contemporary Mathematics, V.517, July 2010.
(with V Moll, A Straub)
One-loop correction integrals for orthopositronium lifetimes in QED,
J Math. Physics, #50, 2009.
(with G Heinig)
Is every complex matrix similar to a Toeplitz matrix?
Birkhauser, V.199, Jan. 2010. In memoriam,
Georg Heinig, a wonderful Mensch!
(with R P Stanley)
Polynomial coefficient enumeration, preprint.
A note on Fibonacci-type polynomials, J. of INTEGERS, #A2, 10 (2010).
(with A. Straub, V.H. Moll)
Valuation of k-binomial coefficients, Acta Arithmetica, #149,
2009, 31-42.
(with V H Moll)
Tapas in Experimental Mathematics
- this book is V. 457, AMS Contemporary Math, 2008.
(with V.H. Moll)
A dozen integrals: Russell-style
Math Newsletter, Ramanujan Math Soc, Vol 18, #1 June 2008.
(with L. Medina, V.H. Moll)
p-adic asymptotic analysis. Proc. Amer. Math. Soc., v.137, #3,
March 2009.
(with O. Espinosa, V.H. Moll)
Laplace transform of the digamma function: integral due to
Glasser-Manna-Oloa, Proc. Amer. Math. Soc., 136 (2008).
Integrals in
Gradshteyn & Ryzhik:
Part 5 and
Part 7 and
Part 9 and
Entry 3.411.5.
(with D. Zeilberger)
"Trivializing" generalizations of some Izergin-Korepin-type determinants.
Discrete Math. & Theor. Comp. Sci. 9 (2007), Nancy, France.
(with L. Medina, V.H.Moll)
A dynamical system of arctangent sequence,
Jour. Number Theory, 128 (2008).
(with V.H.Moll)
A formula for quartic integral: old and new proofs.
The Ramanujan Journal, Oct. 2007.
(with V.H.Moll, D. Manna)
2-adic valuation of Stirling Numbers
Vol. 17, #1, 2008, Experimental
Mathematics.
(with V.H.Moll, D. Manna)
2-adic valuations arising from rational integral
J. Combin. Theory Ser. A, Vol. 115, #8, 2008.
Umemura polynomials associated to Painleve III
also available at
Physics Letters A 354 (2006)
(with A. Ayyer)
Towards the moduli space of extended partial isometries
(with W. Marszalek, R. Riaza)
Singularity
crossing phenomena in DAEs:
a 2-phase fluid flow appl. case study.
Int. J. Comp. Math. Appl., (49) 2-3, 2005.
Cylindrically symmetric solution approaching
Einstein's Universe. J. Geometry & Topology, vol. 2, (3) 2002.
Two Symmetry Problems in Potential Theory. June
6, 2001.
(with D. Zeilberger)
Determinants Through The Looking Glass.
Its companion Maple package is:
DODGSON. Adv. Appl. Math., (27) #2/3, 2001 (special issue.)
A brief commentary for the general reader at:
Online MAA.
A Determinant of the Chudnovskys: Generalizing the Elliptic Frobenius-
Stickelberger-Cauchy Determinantal Identity.
(Elec. J. Comb. 2000.)
(with D. Zeilberger)
q-Apery Irrationality Proofs by q-WZ Pairs.
(with D. Zeilberger)
Hypergeometric Series Acceleration via the WZ Method.
(with S.B. Ekhad)
A Condensed Condensation Proof of a Determinant Evaluation
Conjectured by
Greg
Kuperberg
and Jim Propp.
(with G. Porru, S.Vernier-Piro)
Maximum principles for a class of nonlinear 2nd order elliptic PDEs.
(with M. Zeleke)
On Injectivity of Combinatorial Radon Transform of Order Five.
Faster and Faster convergent series for Zeta(3).
An integral inequality for a class of elliptic operators of 4th order,
Rendiconti Seminario Fac Sc., Univ Cagl, Vol 60, #2: MR 92k
35078.
(with G.Porru) Integral inequalities for linear elliptic operators of 2nd
order, Ricerche di Matematica, Napoli, Vol XXXVII #1: MR 90k
35045.
(with G.Heinig) On the inverses of Hankel & Toeplitz Mosaic matrices,
Seminar Analysis, Academic-Verlag, Berlin: MR 90j 15007.
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