Computation of poisson type integrals

Nonabsolutely convergent Poisson integrals

If a function f has finite Henstock integral on the boundary of the unit disk of R 2 then its Poisson integral exists for |z| < 1 and is o((1 − |z|) −1) as |z| → 1 −. It is shown that this is the best possible uniform pointwise estimate. For an L 1 measure the best estimate is O((1 − |z|) −1). In this paper we consider estimates of Poisson integrals on the unit circle with respect to Alexiewicz...

Computation of Gröbner Bases for Two-Loop Propagator Type Integrals

The most efficient algorithms to evaluate Feynman diagrams exploit recursive methods based on integration by parts technique [2] or technique of generalized recurrence relations [3], [4]. It is easy to derive hundreds of recurrence relations but it is by far not so easy to formulate optimal algorithm how to use them for the reduction of a given type of integrals to a minimal set of basis integr...

Computation of contour integrals

Computation of Fresnel Integrals

This paper describes a method for spreadsheet computations of Fresnel integrals to six significant figures, based on successive improvements of known rational approximations which are accurate to only three figures. Outside the range of validity of the improved approximations, known series expansions are used to obtain the Fresnel integrals to six figures.

Computation of Feynman loop integrals

We address multivariate integration and extrapolation techniques for the computation of Feynman loop integrals. Loop integrals are required for perturbation calculations in high energy physics, as they contribute corrections to the scattering amplitude and the cross section for the collision of elementary particles. We use iterated integration to calculate the multivariate integrals. The combin...