Related papers: Recurrence relations of Li coefficients

The 3-term recurrence relation for Hermite polynomials was recently generalized to a recurrence relation for Wronskians of Hermite polynomials. In this note, a similar generalization for Laguerre polynomials is obtained.

Six families of generalized hypergeometric series in a variable $x$ and an arbitrary number of parameters are considered. Each of them is indexed by an integer $n$. Linear recurrence relations in $n$ relate these functions and their product…

Second order recurrence relations of real numbers arise form various applications in discrete time dynamical systems as well as in the context on Markov chains. Solutions to the recurrence relations are fully defined by the first two…

Assuming that the two integrals in the Change of Variable Formula for the Riemann integral on the real line are finite, one can rightfully ask if they have equal value. We give a positive answer to this question. The proof is very easy to…

We consider two algorithms which can be used for proving positivity of sequences that are defined by a linear recurrence equation with polynomial coefficients (P-finite sequences). Both algorithms have in common that while they do succeed…

The central idea of this article is to present a systematic approach to construct some recurrence relations for the solutions of the second-order linear difference equation of hypergeometric-type defined on the quadratic-type lattices. We…

We investigate semi-classical generalizations of the Charlier and Meixner polynomials, which are discrete orthogonal polynomials that satisfy three-term recurrence relations. It is shown that the coefficients in these recurrence relations…

We define a generalisation of the completed Riemann zeta function in several complex variables. It satisfies a functional equation, shuffle product identities, and has simple poles along finitely many hyperplanes, with a recursive structure…

We reexamine the Riemann Rearrangement Theorem for different types of convergence. We consider series convergence with respect to a filter. We describe the Sum Range (SR) of a series along the 2n-filter and for statistically convergent…

Let X be a subshift satisfy non-uniform structure. In this paper, we give quantitative estimate of the recurrence sets. These results can be applied to a large class of symbolic systems, including beta-shifts, S-gap shifts and their…

This is a short note about Schur positivity. We introduce Schur polynomials and explain how they appear in the representation theory of the general linear group. We end with a new result of the author with F. Bergeron and V. Reiner that…

In previous work of the authors, we investigated the Born and inverse Born series for a scalar wave equation with linear and nonlinear terms, the nonlinearity being cubic of Kerr type [8]. We reported conditions which guarantee convergence…

The object of this paper is to generalize a theorem on the binomial coefficient [4] to the case in an arithmetic progression. We will also give a slightly stronger result than Langevin's [2].

New differential-recurrence properties of dual Bernstein polynomials are given which follow from relations between dual Bernstein and orthogonal Hahn and Jacobi polynomials. Using these results, a fourth-order differential equation…

We give recurrence relations for any family of generalized Appell polynomials unifying so some known recurrences of many classical sequences of polynomials. Our main tool to get our goal is the Riordan group. We use the product of Riordan…

The systematic approach to solving the recurrence relations for multi-loop integrals is described. In particular, the criteria of their reducibility is suggested.

We develop the $L$-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of quadratic twist of modular $L$-functions using multiple Dirichlet series under the generalized Riemann…

In the paper, the author derives several "diagonal" recurrence relations, constructs some inequalities, finds monotonicity, and poses a conjecture related to Stirling numbers of the second kind.

In this article, we set up a method of reconstructing to polylogarithms $\mathrm{Li}_k(z)$ from zeta values $\zeta(k)$ via the Riemann-Hilbert problem. This is referred to as "a recursive Riemann-Hilbert problem of additive type." Moreover,…

Using the method of multiple Dirichlet series, we develop L-functions ratios conjecture with one shift in both the numerator and denominator in certain ranges for quadratic families of Dirichlet and Hecke L-functions of primerelated moduli…