Related papers: Analytic Continuation for Multiple Zeta Values usi…
The symbolic method is used to get explicit formulae for the products or powers of Bessel functions and for the relevant integrals.
In this paper we use the generating functions and the double shuffle relations satisfied the multiple zeta values to derive some new families of identities.
We approach Riordan arrays and their generalizations via umbral symbolic methods. This new approach allows us to derive fundamental aspects of the theory of Riordan arrays as immediate consequences of the umbral version of the classical…
We supplement a very recent paper of R. Crandall concerned with the multiprecision computation of several important special functions and numbers. We show an alternative series representation for the Riemann and Hurwitz zeta functions…
We present a concise method for deriving an explicit formula for $p$-adic multiple zeta values. The formula features a variant of multiple harmonic sums, termed binomial multiple harmonic sums.
It is known that local zeta functions associated with real analytic functions can be analytically continued as meromorphic functions to the hole complex plane. In this paper, certain cases of specific (non-real analytic) smooth functions…
Influence diagrams provide a compact graphical representation of decision problems. Several algorithms for the quick computation of their associated expected utilities are available in the literature. However, often they rely on a full…
Colored multiple zeta values are special values of multiple polylogarithms evaluated at Nth roots of unity. In this paper, we define both the finite and the symmetrized versions of these values and show that they both satisfy the double…
Given a holomorphic iterated function scheme with a finite symmetry group $G$, we show that the associated dynamical zeta function factorizes into symmetry-reduced analytic zeta functions that are parametrized by the unitary irreducible…
We have gone back to old methods found in the historical part of Hardy's Divergent Series well before the invention of the modern analytic continuation to use formal manipulation of harmonic sums which produce some interesting formulae.…
A symbolic method is used to establish some properties of the Bernoulli-Barnes polynomials.
In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…
In this paper, we present new explicit simultaneous rational approximations converging sub-exponentially to the values of Bell polynomials at the points of the form $(\gamma, 1! (2a+1)\zeta(2), 2!\zeta(3),..., (m-1)!(a+1+(-1)^ma)\zeta(m)),$…
In this paper, for any positive integer $\ell\geq2,$ we define $\ell$-generalized Fibonacci zeta function. We then study its analytic continuation to the whole complex plane $\mathbb{C}.$ Further, we compute a possible list of singularities…
The sum formulas for multiple zeta(-star) values and symmetric multiple zeta(-star) values bear a striking resemblance. We explain the resemblance in a rather straightforward manner using an identity that involves the Schur multiple zeta…
We provide a framework for relating certain q-series defined by sums over partitions to multiple zeta values. In particular, we introduce a space of polynomial functions on partitions for which the associated q-series are q-analogues of…
Two representations of the Bessel zeta function are investigated. An incomplete representation is constructed using contour integration and an integral representation due to Hawkins is fully evaluated (analytically continued) to produce two…
This paper presents a general and systematic discussion of various symbolic representations of iterated maps through subshifts. We give a unified model for all continuous maps on a metric space, by representing a map through a general…
We describe in this work all solutions to the problem of renormalizing multiple zeta values at arguments of any sign in a quasi-shuffle compatible way. As a corollary we clarify the relation between different renormalizations at…
In this paper, we give the values of a certain kind of $q$-multiple zeta functions at roots of unity. Various multiple zeta values have been proposed and studied by many researchers, but these multiple zeta values naturally arise from…