We present the program BOKASUN for fast and precise evaluation of the Master Integrals of the two-loop self-mass sunrise diagram for arbitrary values of the internal masses and the external four-momentum. We use a combination of two methods: a Bernoulli accelerated series expansion and a Runge-Kutta numerical solution of a system of linear differential equations. PACS: 11.15.Bt

We give series expansions for the Barnes multiple zeta functions in terms of rational functions whose numerators are complex-order Bernoulli polynomials, and whose denominators are linear. We also derive corresponding rational expansions for Dirichlet L-functions and multiple log gamma functions in terms of higher order Bernoulli polynomials. These expansions naturally express many of the well-...

Methods and an algorithm for computing the generalized Marcum Q−function (Qµ(x, y)) and the complementary function (Pµ(x, y)) are described. These functions appear in problems of different technical and scientific areas such as, for example, radar detection and communications, statistics and probability theory , where they are called the non-central chi-square or the non central gamma cumulativ...

We develop a method for pricing financial options under uncertain volatility. The method is based on the dynamic programming principle and a Fourier cosine expansion method. Local errors in the vicinity of domain boundaries, originating from the use of Fourier series expansions, may hamper the algorithm’s convergence. We use an extrapolation method to deal with these errors.

This paper proposes a method to obtain optimal 2-order approximation preserving prefilters for a given orthogonal unbalanced multiwavelet basis. This procedure uses the prefilter construction introduced in [3]. The prefilter optimization scheme exploits the Taylor series expansion of the prefilter combined with the multiwavelet. Using the DGHM multiwavelet with the obtained optimal prefilter, w...

We present a novel approach for the fast approximation of the discrete Gauss transform in higher dimensions. The algorithm is based on the dual-tree technique and introduces a new Taylor series expansion. It compares favorably to existing methods especially when it comes to higher dimensions and a broad range of bandwidths. Numerical results with different datasets in up to 62 dimensions demons...

We point out that the matter profile effect—the effect of matter density fluctuation on the baseline—is very important to estimate the parameters in a neutrino factory with a very long baseline. To make it clear, we propose the method of Fourier series expansion of the matter profile. By using this method, we can take account of both the matter profile effect and its ambiguity. For very long ba...

Dealing with non-linear distortion in fingerprint images is a major difficulty for automated fingerprint verification systems. While this distortion can be a nuisance in minutiae matching systems, it is a major concern when matching smaller structures, such as points along ridges and pore locations. In this paper we show that a simple transformation derived from a Taylor series expansion can be...

We describe the q–Engel series expansion for Laurent series discovered by John Knopfmacher and use this algorithm to shed new light on partition identities related to two entries from Slater’s list. In our study Al-Salam/Ismail and Santos polynomials play a crucial rôle. Dedicated to the memory of John Knopfmacher 1937–1999