Determinants through the looking glass (2009)
Tewodros Amdeberhan, Doron Zeilberger
dedicated to dominique foata on his 65th birthday Using a recurrence derived from Dodgson’s Condensation Method, we provide numerous explicit evaluations of determinants. They were all conjectured,...
A note on a question due to A. Garsia (2009)
Adriano Garsia has provided an explicit formula to enumerate a certain class of permutations in the symmetric group S_n. In this short note, we prove a stronger version of the assertion under a...
Tewodros Amdeberhan, Doron Zeilberger, Xi Yj Axiyj
Abstract. We generalize (and hence trivialize and routinize) numerous explicit evaluations of determinants and pfaffians due to Kuperberg, as well as a determinant of Tsuchiya. The level of...
A note on Fibonacci-type polynomials (2008)
We opt to study the convergence of maximal real roots of certain Fibonacci-type polynomials given by $G_n=x^kG_{n-1}+G_{n-2}$. The special cases $k=1$ and $k=2$ are found in [4] and [7], respectively.
Polynomial Coefficient Enumeration (2008)
Amdeberhan, Tewodros, Stanley, Richard P.
Let $f(x_1,...,x_k)$ be a polynomial over a field $K$. This paper considers such questions as the enumeration of the number of nonzero coefficients of $f$ or of the number of coefficients equal to...
The p-adic valuation of k-central binomial coefficients (2008)
Straub, Armin, Amdeberhan, Tewodros, Moll, Victor H.
The coefficients c(n,k) defined by (1-k^2x)^(-1/k) = sum c(n,k) x^n reduce to the central binomial coefficients for k=2. Motivated by a question of H. Montgomery and H. Shapiro for the case k=3, we...
A dozen integrals: Russell-style (2008)
Amdeberhan, Tewodros, Moll, Victor
On June 15, 1876, the Proceedings of the Royal Society of London published a paper by Mr. W. H. L. Russell entitled "On certain integrals". The paper starts with "The following are certain integrals...
Differential operators, shifted parts, and hook lengths (2008)
We discuss Sekiguchi-type differential operators, their eigenvalues, and a generalization of Andrews-Goulden-Jackson formula. These will be applied to extract explicit formulae involving shifted...
Abstract. D.V. Chudnovsky and G.V. Chudnovsky [CH] introduced a generalization of the Frobenius-Stickelberger determinantal identity involving elliptic functions that generalize the Cauchy...
Abstract. Using WZ pairs we present accelerated series for computing i(3) AMS Subject Classification: Primary 05A Alf van der Poorten [P] gave a delightful account of Ap'ery's proof [A] of...
The Laplace transform of the digamma function: an integral due to Glasser, Manna and Oloa (2007)
Amdeberhan, Tewodros, Moll, Victor H.
We provide an analytic expression for the Laplace transform of the digamma fuction. This complements work of L. Glasser, D. Manna and O. Oloa on this question. The Laplace transform is continuous in...
The 2-adic valuations of Stirling numbers (2007)
Amdeberhan, Tewodros, Manna, Dante, Moll, Victor H.
The 2-adic valuation of the Stirling numbres is examined. We conjecture pattrens about the distributions of these valuations in residue classes modulo powers of 2.
The integrals in Gradshteyn and Ryzhik. Part 7: Elementary examples (2007)
Amdeberhan, Tewodros, Moll, Victor H.
The classical table of integrals by I. S. Gradshteyn and I. M. Ryzhik contains some elementary integrals. We discuss their evaluations.
Amdeberhan, Tewodros, Moll, Victor H., Rosenberg, Jason, Straub, Armin, Whitworth, Pat
The classical table of integrals by I. S. Gradshteyn and I. M. Ryzhik contains many definite integrals where the integrand is the product of a rational function times the logarithm of another...
A formula for a quartic integral: a survey of old proofs and some new ones (2007)
Amdeberhan, Tewodros, Moll, Victor H.
We discuss several existing proofs of the value of a quartic integral and present a new proof that evolved from rational Landen transformations.
The 2-adic valuation of a sequence arising from a rational integral (2007)
Amdeberhan, Tewodros, Manna, Dante, Moll, Victor H.
We analyze properties of the 2-adic valuations of an integer sequence that originates from an explicit evaluation of a quartic integral. We also give a combinatorial interpretation of the valuations...
The integrals in Gradshteyn and Ryzhik. Part 5: Some trigonometric integrals (2007)
Amdeberhan, Tewodros, Medina, Luis, Moll, Victor H.
We present evalauations and provide proofs of definite integrals involving the function x^p cos^n x. These formulae are generalizations of 3.761.11 and 3.822.1, among others, in the classical table...
TrivializingGeneralizations of some Izergin-Korepin-type Determinants (2007)
Tewodros Amdeberhan, Doron Zeilberger
We generalize (and hence trivialize and routinize) numerous explicit evaluations of determinants and pfaffians due to Kuperberg, as well as a determinant of Tsuchiya. The level of generality of our...
Towards The Moduli Space of Extended Partial Isometries (2005)
Amdeberhan, Tewodros, Ayyer, Arvind
Partial Isometries are important constructs that help give nontrivial solutions once a simple solution is known. We generalize this notion to Extended Partial Isometries and include operators which...
Two symmetry problems in potential theory (2001)
We consider two eliiptic overdetermined boundary value problems. There are variants on J. Serrin's 1971 classical results and having the same conclusion that the domains should be forcibly Euclidean...
Two symmetry problems in potential theory (2001)
We consider two overdetermined boundary value problems as variants on J. Serrin's 1971 classical results and prove in both cases that the domains must be Euclidean balls.
Amdeberhan, Tewodros, Ekhad, Shalosh B.
We give a generalization and a short mechanized proof of determinant conjectured by G. Kuperberg and J. Propp. Further generalizations and applications of the method to some q-analogues may be found...
Maximum principles for a class of nonlinear second order elliptic differential equations (1998)
Porru, Giovanni, Amdeberhan, Tewodros, Vernier-Piro, S.
In this paper we investigate maximum principles for functionals defined on solutions to special partial differential equations of elliptic type, extending results by Payne and Philippin. We apply...
Faster and Faster convergent series for $\zeta(3)$ (1998)
Using WZ pairs we present an infinite family of accelerated series for computing $\zeta(3)$.
Hypergeometric Series Acceleration Via the WZ method (1998)
Amdeberhan, Tewodros, Zeilberger, Doron
Based on the WZ method, some series acceleration formulas are given. These formulas allow to write down an infinite family of parametrized identities from any given identity of WZ type. Further, this...
q-Apery Irrationality Proofs by q-WZ Pairs (1998)
Amdeberhan, Tewodros, Zeilberger, Doron
Using WZ forms, Apery-style proofs of the irrationality of the q-analogues of the Harmonic seires and Ln(2) are given. For the q-analogue of Ln(2), this method of proof produces an improved...
Hypergeometric series acceleration via the WZ method (1997)
Tewodros Amdeberhan, Doron Zeilberger, Typeset Ams-tex
Dedicated to Herb Wilf on his one million-first birthday Abstract. Based on the WZ method, some series acceleration formulas are given. These formulas allow us to write down an infinite family of...
Tewodros Amdeberhan, Shalosh B. Ekhad, Greg Kuperberg
[P] have conjectured the following determinant identity:
ARTICLE NO. AM970565 q-Apery ´ Irrationality Proofs by q-WZ Pairs (1997)
Tewodros Amdeberhan, Doron Zeilberger
Using WZ pairs, Apery-style ´ proofs of the irrationality of the q-analogues of the Harmonic series and LnŽ. 2 are given. For the q-analogue of LnŽ. 2, this method produces an improved...
Hypergeometric Series Acceleration via the WZ Method (1996)
Tewodros Amdeberhan, Doron Zeilberger
. Based on the WZ method, some series acceleration formulas are given. These formulas allow us to write down an infinite family of parametrized identities from any given identity of WZ type. Further,...
Faster And Faster Convergent Series For ... (1996)
. Using WZ pairs we present accelerated series for computing i(3) AMS Subject Classification: Primary 05A Alf van der Poorten [P] gave a delightful account of Ap'ery's proof [A] of the...