Related papers: Some integrals related to the Basel problem

On the basis of the relativistic kinetic theory the relativistic statistical systems with scalar interaction particles are investigated. The self-consistent system of the equations describing self-gravitating plasma with interpartial scalar…

We compute approximate solutions to inverse problems for determining parameters in differential equation models with stochastic data on output quantities. The formulation of the problem and modeling framework define a solution as a…

We present a method using contour integration to derive definite integrals and their associated infinite sums which can be expressed as a special function. We give a proof of the basic equation and some examples of the method. The advantage…

This paper studies the problem of testing whether a system of linear equality and inequality constraints admits a solution when the coefficients of that system may have to be estimated. We show that a wide range of inferential questions in…

Computers are good at evaluating finite sums in closed form, but there are finite sums which do not have closed forms. Summands which do not produce a closed form can often be ``fixed'' by multiplying them by a suitable polynomial. We…

We study representations of a random variable $\xi$ as an integral of an adapted process with respect to the Lebesgue measure. The existence of such representations in two different regularity classes is characterized in terms of the…

We obtain asymptotic results for well known summatory arithmetic functions, such as $\psi(x),$ and establish connections to new summatory functions. A new Volterra integral equation is offered, which is solved by summatory arithmetic…

We present integral representations of solutions to division problems involving matrices of polynomials in several complex variables. We also find estimates of the polynomial degree of the solutions by means of careful degree estimates of…

An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with…

The work is devoted to the construction of a new interval arithmetic which would combine algorithmic efficiency and high quality estimation of the ranges of expressions.

We derive global analytic representations of fundamental solutions for a class of linear parabolic systems with full coupling of first order derivative terms where coefficient may depend on space and time. Pointwise convergence of the…

We give evaluations in closed form of certain Lehmer-binomial series

We present the evaluation of a family of logarithmic integrals. This provides a unified proof of several formulas in the classical table of integrals by I. S. Gradshteyn and I. M. Rhyzik.

In this paper, we investigate traces of cycle integrals of certain meromorphic modular forms. By relating them to regularised theta lifts we provide explicit formulae for them in terms of coefficients of harmonic Maass forms.

Using some new logarithmic formal calculus, we construct a well known vertex algebra, obtaining the Jacobi identity directly, in an essentially self-contained treatment.

In this article we prove some identities which allow us to evaluate some multiple unit square integrals. In our examples we will give the value of some double and triple integrals. Then, we prove several classical integral formulas with the…

In this note we derive some interesting definite integrals involving Malmsten logarithm forms, reciprocal logarithm forms and K\"{o}lbig type integrals in terms of special functions.

By doing a slight change to a beautiful and widely unknown argument by E. L. Stark [E. L. Stark, Application of a Mean Value Theorem for Integrals to Series Summation, Amer. Math. Monthly 85 (1978) 481--483.] we get a candidate to be…

The problem of quantizing theories defined over configuration spaces described by non-commuting parameters is considered. In this paper we describe the first step in this direction, that is the definition of an integral over a general…

Cyclotomic polylogarithms are reviewed and new results concerning the special constants that occur are presented. This also allows some comments on previous literature results using PSLQ.