On certain Definite 9-Function Integrals

Numerical Calculation of Certain Definite Integrals by Poisson's Summation Formula

It is generally agreed that of all quadrature formulae, the trapezoidal rule, while being the simplest, is also the least accurate. There is, however, a rather general class of integrals for which the trapezoidal rule can be shown to be a highly accurate means of obtaining numerical values. Specifically, if the integrand is a periodic, even function with all derivatives continuous, then the int...

Numerical Calculation of Certain Definite Integrals by Poisson's Summation Formula

It is generally agreed that of all quadrature formulae, the trapezoidal rule, while being the simplest, is also the least accurate. There is, however, a rather general class of integrals for which the trapezoidal rule can be shown to be a highly accurate means of obtaining numerical values. Specifically, if the integrand is a periodic, even function with all derivatives continuous, then the int...

On Some Definite Integrals Involving the Hurwitz Zeta Function

We establish a series of integral formulae involving the Hurwitz zeta function. Applications are given to integrals of Bernoulli polynomials, log Γ(q) and log sin(q).

Some Definite Integrals Associated with the Riemann Zeta Function

Certain Positive-definite Kernels

In one way or another, the extension of the standard Brownian motion process {B¡: t e [0,oo)} to a (Gaussian) random field {Bt: t € R+} involves a proof of the positive semi-definiteness of the kernel used to generalize p(s, 1) = cov(Bs,B¡) = s A t to multidimensional time. Simple direct analytical proofs are provided here for the cases of (i) the Levy multiparameter Brownian motion, (ii) the C...