Related papers: A note on Sonnenschein summability matrices
A short introduction is given to the method of light-cone sum rules, their theoretical background and main modifications. The discussion is concentrated but not restricted to the applications to heavy quark decays.
By combining the telescoping method with an algebraic relation, four classes of binomial moments are examined. Several explicit summation formulae are established.
This note deals with a simultaneous approximation of several matrices by a finite family of diagonalizable matrices satisfying an additional condition for the spectrum of a matrix product. That is the simplicity of all eigenvalues.
We use Poisson summation formula to calculate integrals of producs of sinc functions (cf. [4]) and related integrals as in [5] and [3]. We also generalize the one in [5] and introduce other remarkable integrals. Finally we give a sum…
A new simple geometric method is presented for finding the exact value of $\sum_{n=1}^\infty 1/n^2$.
We give a combinatorial proof of a formula giving the partial sums of the $k$-bonacci sequence as alternating sums of powers of two multiplied by binomial coefficients. As a corollary we obtain a formula for the $k$-bonacci numbers.
We provide numerical procedures for possibly best evaluating the sum of positive series. Our procedures are based on the application of a generalized version of Kummer's test.
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
Writing the values of Krawtchouk polynomials as matrices, we consider weighted partial sums along columns. For the general case, we find an identity that, in the symmetric case yields a formula for such partial sums. Complete sums of…
We study multiplicative nested sums, which are generalizations of harmonic sums, and provide a calculation through multiplication of index matrices. Special cases interpret the index matrices as stochastic transition matrices of random…
We describe a dynamic programming algorithm for exact counting and exact uniform sampling of matrices with specified row and column sums. The algorithm runs in polynomial time when the column sums are bounded. Binary or non-negative integer…
We introduce Euler summability method for sequences of fuzzy numbers and state a Tauberian theorem concerning Euler summability method, of which proof provides an alternative to that of K. Knopp[\"Uber das Eulersche Summierungsverfahren II,…
We solve an elementary number theory problem on sums of fractional parts, using methods from group theory. We apply our result to deduce the finiteness of certain monodromy representations.
We define a general notion of "summability" of a set $I\subseteq\mathbb{C^{N}}$ and show that some trivial condition necessary for a set to be summable, is also sufficient. We deduce some intresting corollaries.
We show that sums of carefully chosen coincidence rates in a multiphoton interferometry experiment can be simplified by replacing the original unitary scattering matrix with a coset matrix containing $0$s. The number and placement of these…
We propose a numerical method, based upon matrix-pencils, for the identification of parameters and coefficients of a monomial-exponential sum. We note that this method can be considered an extension of the numerical methods for the…
In this article, we give a formula for the generalization of the binomial coefficient to the complex numbers as a linear combination of $\sinc$ functions. We then give a general formula to compute the integral on the real line of the…
We derive and prove an explicit formula for the sum of the fractional parts of certain geometric series. Although the proof is straightforward, we have been unable to locate any reference to this result. This summation formula allows us to…
We discuss various aspects of representation of a polynomial as a sum of monomials (for example, uniqueness of such representation and related estimations).
This paper presents a combinatorial study of sums of integer powers of the cotangent which is a popular theme in classical calculus. Our main tool the realization of cotangent values as eigenvalues of a simple self-adjoint matrix with…