Papers by Victor H. Moll

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• The Cauchy-Schlomilch transformation
  (with T. Amdeberhan, L. Glasser, M. C. Jones, R. Posey and D. Varela)
  Integral Transforms and Special Functions 30, 2019, 940-961.

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• A closed-form solution might be given by a tree. Valuations of quadratic polynomials
  (with L. Almodovar, A. Byrnes, J. Fink, X. Guan, A. Kerarwani, G. Lavigne, L. Medina,
  I. Nogues, S. Rajasekaran, E. Rowland and A. Yuan)
  Scientia, Series A: Math. Sciences 29, 2019, 11-28.

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• Extensions of set partitions and permutations
  (with J. Caicedo, J. L. Ramirez and D. Villamizar).
  Elec. Jour. Combinatorics 26, 2019, #P2.20.
  

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• The arithmetic-harmonic mean and Landen transformations
  Scientia, Series A: Math. Sciences 29, 2019, 1-5.

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• A warning about symbolic integration
  (with D. S. Bernstein).
  Scientia, Series A: Math. Sciences 29, 2019, 7-9.

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• A symbolic approach to multiple zeta values at the negative integers
  (with L. Jiu and C. Vignat).
  Journal of Symbolic Computation 84, 2018, 1-13.

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• Sums of four or fewer squares
  (with A. Kesarwani).
  Scientia, Series A: Math. Sciences 28, 2018, 55-62.

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• Combinatorial and arithmetical properties of the restricted and associated Bell and factorial numbers
  (with J. L. Ramirez and D. Villamizar).
  Journal of Combinatorics 9, 2018, 693-720.
  

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• A generalized modified Bessel function and a higher level analogue of the theta transformation formula
  (with A. Dixit, A. Kesarwani and an appendix by N. Temme)
  Journal of Math. Anal. and Applications 459, 2018, 385-418.
  

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• Periodicity in the p-adic valuation of a polynomial
  (with L. Medina and E. Rowland)
  Journal of Number Theory 180, 2017, 139-153.
  

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• Integrals of Frullani type and the method of brackets
  (with S. Bravo, I. Gonzalez and K.Kohl)
  Open Mathematics 15, 2017, 1-12.
  

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• An extension of the method of brackets
  (with I. Gonzalez, K.Kohl and L. Jiu)
  Open Mathematics 15, 2017, 1181-1211.
  

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• The moments of the hydrogen atom by the method of brackets
  (with I. Gonzalez, K. Kohl, I. Kondrashuk and D. Salinas)
  SIGMA 13, 2017, 1-13.

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• Modified Norlund polynomials
  (with A. Dixit, A. Kabza and C. Vignat)
  The Ramanujan Journal 42, 2017, 69-96.

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• Asymptotics and exact formulas for Zagier polynomials
  (with A. Dixit, M. L. Glasser, C. Vignat)
  Res. Number Theory 12, 2016, 47-74.

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• A series involving Catalan numbers. Proofs and demonstrations
  (with T. Amdeberhan, X. Guan, L. Jiu and C. Vignat)
  Elemente der Mathematik 71, 2016, 109-121.

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• Pochhammer symbols with negative indices. A new rule for the method of brackets
  (with I. Gonzalez and L Jiu)
  Open Mathematics 14, 2016, 681-686.
  

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• Infinite products arising in paperfolding.
  (with L. Almodovar, F. Roman, E. Rowland, H. Quan and M. Washington)
  Journal of Integer Sequences 19, 2016, article 16.5.1
  

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• A symbolic approach to some Bernoulli-Barnes polynomials
  (with L. Jiu and C. Vignat)
  International Journal of Number Theory 12, 2016, 109-121.

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• A hypergeometric inequality
  (with A. Dixit and V. Pillwein)
  Journal of Analytic Combinatorics 20, 2016, 65-72.

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• Involutions and their progenies
  (with T. Amdeberhan)
  Journal of Combinatorics 6, 2016, 483-508.

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• Self-reciprocal functions, powers of the Riemann zeta function and modular-type transformations
  (with A. Dixit)
  Journal of Number Theory 147, 2015, 211-249.
  

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• The finite Fourier transform of classical polynomials
  (with Atul Dixit, Lin Jiu and Christophe Vignat)
  Journal of the Australian Mathematical Society 98, 2015, 145-160.
  

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• A probabilistic approach to some binomial identities
  (with C. Vignat)
  Elemente der Mathematik 70, 2015, 55-66.

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• A by-product of an integral evaluation
  (with T. Amdeberhan).
  The Ramanujan Journal 37, 2015, 219-222.

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• Generalized Bernoulli numbers and a formula of Lucas
  (with Christophe Vignat)
  The Fibonacci Quarterly 53, 2015, 349-359.

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• Identities for generalized Euler polynomials
  (with Lin Jiu and Christophe Vignat)
  Integral Transforms and Special Functions 25, 2014, 777-789.

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• Generalized Fibonacci polynomials and Fibonomial coefficients
  (with T. Amdeberhan, X. Chen and B. Sagan)
  Annals of Combinatorics 18, 2014, 541-562.

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• On polynomials connected to powers of Bessel functions
  (with C. Vignat)
  International Journal of Number Theory 10, 2014, 1245-1257.

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• Recursion rules for the hypergeometric zeta function
  (with A. Byrnes, Lin Jiu and C. Vignat)
  International Journal of Number Theory 7, 2014, 1761-1782.

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• The unimodality of a polynomial coming from a rational integral. Back to the original proof
  (with T. Amdeberhan, A. Dixit, Xiao Guan and Lin Jiu)
  Journal of Math. Anal. and Applications   420, 2014, 1154-1166.
  

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• A special rational function with vanishing integral
  Integral Transforms and Special Functions 24, 2014, 970-975.
  

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• Evaluation of entries in Gradshteyn and Ryzhik employing the method of brackets
  (with I. Gonzalez and K. Kohl).
  Scientia, Series A: Math. Sciences 25, 2014, 65-84.

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• The Zagier polynomials. Part II: arithmetic properties of coefficients.
  (with M. Coffey, V. De Angelis, A. Dixit, A. Straub and C. Vignat)
  The Ramanujan Journal 35, 2014, 361-390.

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• The Zagier modification of Bernoulli numbers and a polynomial extension. Part I.
  (with A. Dixit and C. Vignat)
  The Ramanujan Journal 33, 2014, 379-422.
  

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• An arithmetic conjecture on a sequence of arctangent sums
  Scientia, Series A: Math. Sciences 24, 2013, 90-119.

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• From sequences to polynomials and back, via operator orderings
  (with T. Amdeberhan, V. De Angelis, A. Dixit, and C. Vignat)
  Journal of Mathematical Physics 54, 2013, 123502.

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• Valuations and combinatorics of truncated exponential sums
  (with T. Amdeberhan and D. Callan)
  INTEGERS, Volume 13, A21, 2013.

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• A probabilistic interpretation of a sequence related to Narayana polynomials
  (with T. Amdeberhan and C. Vignat)
  Online Journal of Analytic Combinatorics 8, Paper 3, 2013.

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• A family of palindromic polynomials
  (with T. Amdeberhan and V. Papanicolau
  Scientia, Series A: Math. Sciences 24, 2013, 25-32.

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• Complementary Bell numbers: Arithmetical properties and Wilf's conjecture
  (with T. Amdeberhan and V. De Angelis)

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• A generalized Ramanujan Master Theorem applied to the evaluation fo Feynman diagrams
  (with I. Gonzalez and I. Schmidt)
  Advances in Applied Mathematics 63, 2015, 214-230.
  

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• Ramanujan Master's Theorem
  (with T. Amdeberhan, O. Espinosa, I. Gonzalez, M. Harrison and A. Straub)
  The Ramanujan Journal 29, 2012, 103-120.
  

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• The p-adic valuation of ASM numbers.
  (with Erin Beyerstedt and Xinyu Sun)
  Journal of Integer Sequences 14, 2011, article 11.8.7
  

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• The iterated integrals of ln(1+x^2)
  (with Tewodros Amdeberhan, Christoph Koutschan and Eric Rowland)
  International Journal of Number Theory 7, 2011, 1-12.
  

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• Broken bracelets, Molien series, paraffin wax and an elliptic curve of conductor 48
  (with T. Amdeberhan and Mahir Can).
  SIAM Journal of Discrete Math. 25, 2011,1843-1859.

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• Arithmetic properties of plane partitions
  (with T. Amdeberhan).
  Elec. Jour. Combinatorics 18, 2011, #R1.
  

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• Solution to Problem 11519
  (with T. Amdeberhan).

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• The evaluation of a quartic integral via Schwinger, Schur and Bessel
  (with T. Amdeberhan and Christophe Vignat).
  The Ramanujan Journal 28, 2012,1-14.

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• A pretty binomial identity
  (with T. Amdeberhan, V. de Angelis, M. Lin and B. Sury).
  Elemente der Mathematik 67, 2012, 1-8.

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• Integrals of powers of loggamma (with Tewodros Amdeberhan, Mark W. Coffey, Olivier Espinosa,
  Christoph Koutschan and Dante V. Manna)
  Proc. Amer. Math. Soc. 139, 2011, 535-545.

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• The action of Hecke operators on hypergeometric functions
  Journal of Australian Mathematical Society 89, 2010, 51-74
  (with Sinai Robins and Kirk Soodhalter).

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• The method of brackets. Part 2: examples and applications (with Ivan Gonzalez and Armin Straub)
  Contemporary Mathematics 517, 157-171, 2010.
  

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• Iterated primitives of logarithmic powers (with Luis Medina and Eric Rowland)
  International Journal of Number Theory 7(3), 623-634, 2011
  

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• The $p$-adic valuation of Stirling numbers (with A. Berrizbeitia, L. Medina, A. Moll and L. Noble)
  Journal for Algebra and Number Theory Academia 1, 2010, 1-30.

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• Wallis-Ramanujan-Schur-Feynman
  (with T. Amdeberhan, O. Espinosa and A. Straub).
  American Mathematical Monthly 117, 2010, 618-632
  

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• A fast numerical algorithm for the integration of rational functions
  (with Dante Manna, Luis Medina and Armin Straub) )
  Numerische Mathematik115, 2010, 289-307.
  

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• Seized opportunities.
  Notices Amer. Math. Soc. 57, 2010, 476-484.
  

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• The evaluation of Tornheim double sums, Part 2 (with Olivier Espinosa)
  The Ramanujan Journal 22, 2010, 55-99.
  

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• Definite integrals by the method of brackets. Part 1. (with Ivan Gonzalez)
  Advances in Applied Mathematics 45, 2010, 50-73.
  

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• Closed-form evaluation of integrals appearing in positronium decay
  (with T. Amdeberhan and A. Straub)
  Journal of Math. Physics 50, 2009, 103528
  

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• The p-adic valuations of sequences counting alternating sign matrices. (with Xinyu Sun)
  Journal of Integer Sequences 12, 2009, Article 09.3.8
  

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• A remarkable sequence of integers (with Dante Manna)
  Expositiones Mathematicae 27, 2009, 289-312.
  

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• The $p$-adic valuation of $k$-central binomial coefficients
  (with Armin Straub and Tewodros Amdeberhan).
  Acta Arithmetica 149, 2009, 31-42.
  

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• A binary tree representation for the 2-adic valuation of a sequence arising from a rational integral
  (with Xinyu Sun).
  Integers 10, 2009, 211-222.

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• A class of logarithmic integrals (with L. Medina).
  Ramanujan Journal 20, 2009, 91-126.
  

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• Asymptotic valuations of sequences satisfying first order recurrences
  (with T. Amdeberhan and L. Medina).
  Proc. Amer. Math. Soc. 137, 2009, 885-890.
  

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• A formula for a quartic integral: a survey of old proofs and some new ones (with T. Amdeberhan).
  Ramanujan Journal 18, 2009, 91-102.
  

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• Solution to Problem 11299
  (with T. Amdeberhan).

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• An iterative method for numerical integration of rational functions (with D. Manna).
  Contemporary Mathematics 471, 2008, 161-174.
  

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• A dozen integrals: Russel style
  (with T. Amdeberhan).
  Ramanujan Mathematics Newsletter 18(1), 2008, 7-8.

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• The Laplace transform of the digamma function: an integral due to Glasser, Manna and Oloa
  (with T. Amdeberhan and O. Espinosa).
  Proc. Amer. Math. Soc. 136, 2008, 3211-3221.
  

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• The $2$-adic valuation of Stirling numbers (with T. Amdeberhan and D. Manna).
  Experimental Mathematics, 17, 2008, 69-82.

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• Landen survey (with D. Manna).
  Probability, Geometry and Integrable Systems
  MSRI Publications 55, 2008, 287-319. Special volume honoring Henry McKean.
  The whole volume can be seen here

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• Integrales definidas: Analisis, Numeros y Experimentos
  Revista Cientifica Tumbaga 2, 2008, 138-174.

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• Arithmetical properties of a sequence arising from an arctangent sum
  Journal of Number Theory 128, 2008, 1808-1847 (with T. Amdeberhan and L. Medina).

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• The $2$-adic valuation of a sequence arising from a rational integral
  (with T. Amdeberhan and D. Manna).
  Journal of Combinatorial Theory, Series A, 115, 2008, 1474-1486.

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• An elementary trigonometric equation
  College Mathematical Journal 39, 2008, 394-398.

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• Combinatorial sequences arising from a rational integral
  Online Journal of Analytic Combinatorics Issue 2, 2007, #4.
  

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• Rational Landen transformations on the real line (with Dante Manna)
  Math Comp 76, 2007, 2023-2043.
  

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• A simple example of a new class of Landen transformations (with Dante Manna)
  American Mathematical Monthly March 2007, 114, 232-241.
  

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• Dynamics of the degree six Landen transformation (with Marc Chamberland)
  Discrete and Continuous Dynamical Systems 15, 2006, 905-919.
  

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• A summation method due to Carr: part 1 (with G. Boros)
  Scientia, Series A: Math. Sciences 12, 2006, 21-37.

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• The evaluation of Tornheim double sums, Part I (with Olivier Espinosa)
  Journal of Number Theory 116, 2006, 200-229.
  

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• Sums of arctangents and some formulas of Ramanujan (with G. Boros)
  Scientia, Series A: Math. Sciences 11, 2005, 13-24.
  

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• An elementary evaluation of a quartic integral (with G. Boros and S. Riley)
  Scientia, Series A: Math. Sciences 11, 2005, 1-12.
  

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• A map on the space of rational functions (with G. Boros, J. Little, E. Mosteig and R. Stanley))
  Rocky Mountain Journal 35, 2005, 1861-1880.
  

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• A generalized polygamma function (with Olivier Espinosa)
  Integral Transforms and Special Functions 15, 2004, 101-115.
  

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• On some families of integrals solvable in terms of polygamma and negapolygamma functions
  (with George Boros and Olivier Espinosa)
  Integral Transforms and Special Functions 14, 2003, 187-203.
  

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• A geometric view of the rational Landen transformation (with John Hubbard)
  Bull. London Math. Soc. 35, 2003, 293-301.
  

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• The evaluation of integrals: a personal story
  Notices Amer. Math. Soc. 49, March 2002, 311-317.
  

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• A transformation of rational functions (with G. Boros and M. Joyce)
  Elemente der Mathematik 57, 2002, 1-11.
  

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• Bernoulli on arc length (with J. Nowalsky, G. Roa and L. Solanilla)
  Math. Magazine 75, 2002, 209-213
  

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• The story of Landen, the hyperbola and the ellipse. (with J. Nowalsky and L. Solanilla)
  Elemente der Mathematik 57, 2002, 19-25.
  

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• On some definite integrals involving the Hurwitz zeta function. Part 2. (with Olivier Espinosa)
  Ramanujan Journal 6, 2002, 449-468.
  

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• On some definite integrals involving the Hurwitz zeta function. Part 1. (with Olivier Espinosa)
  Ramanujan Journal 6, 2002, 159-188.
  

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• Landen transformations and the integration of rational functions. (with George Boros)
  Math Comp 71, 2002, 649-668.
  

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• An integral with three parameters. Part 2. (with George Boros and Roopa Nalam)
  Jour. Comp. Appl. Math. 134, 2001, 113-126.
  

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• An extension of a criterion for unimodality (with J. Alvarez, M. Amadis, G. Boros, D. Karp and L. Rosales)
  Elec. Jour. Combinatorics 8, 2001, #R30.
  

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• The double square root, Jacobi polynomials and Ramanujan's Master Theorem (with George Boros)
  Jour. Comp. Appl. Math. 130, 2001, 337-344.
  

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• The 2-adic valuation of the coefficients of a polynomial (with George Boros and Jeffrey Shallit)
  Scientia, Series A: Math. Sciences 7, 2001, 47-60. Special issue in the memory of Miguel Blazquez.
  

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• A property of Euler's elastic curve. (with P. Neill, J. Nowalsky and L. Solanilla)
  Elemente der Mathematik 55, 2000, 156-162.
  

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• A rational Landen transformation. The case of degree six. (with George Boros)
  Contemporary Mathematics 251, 2000, 83-91.
  

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• The integration of rational functions: examples and problems. Part I. (with George Boros)
  Scientia, Series A: Math. Sciences 6, 2000, 9-28.
  

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• A criterion for unimodality (with George Boros)
  Elec. Jour. Combinatorics 6, 1999, #R10.
  

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• A sequence of unimodal polynomials (with George Boros)
  Journal of Math. Anal. and Applications 237, 1999, 272-287.
  

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• An integral hidden in Gradshteyn and Ryzhik (with George Boros)
  Jour. Comp. Appl. Math. 106, 1999, 361-368.
  

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• An integral with three parameters (with George Boros)
  SIAM Review 40, 1998, 972-980
  

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Victor H. Moll's Home Page