The numerical evaluation of Bessel function integrals may be difficult when the Bessel function is rapidly oscillating in the interval of integration. In the method presented here, the smooth factor of the integrand is replaced by a truncated Chebyshev series approximation and the resulting integral is computed exactly. The numerical aspects of this exact integration are discussed.

Modified clenshaw-curtis method for the computation of Bessel function integrals

On the computation of Fourier transforms of singular functions

In this paper, we extend the Clenshaw-Curtis integration method for the computation of Fourier transform integrals. In particular, we examine the numerical stability of a recurrence relation occurring in this method.

Computation of fourier transform integrals using Chebyshev series expansions

Asymptotic Behaviour of Solutions of Linear Recurrences and Sequences of Möbius-Transformations

It is shown that if the zeros λ 1 , λ 2 ,..., λ n of the polynomial q(λ) = λ n + a 1 λ n−1 +... + a n are distinct and r is an integer in {1, 2,..., n} such that |λ s | ¬= |λ r | if s ¬= r, then the Poincare difference equation y(n + m) + (a 1 + p 1 (m))y(n + m − 1) +... + (a n + p n (m))y(m) = 0 has a solution y r such that (A) y r (m) = λ r m (1 + o(1)) as m → ∞, provided that the sums Σ j=m ∞Pi(j) (1 ≤ i ≤ n) converge sufficiently rapidly. Our results improve over previous results in that these series may converge conditionally, and we give sharper estimates of the o(1) terms in (A)

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Mieke Branders

Papers

The asymptotic behaviour of solutions of difference equations