Computation of infinite integrals involving Bessel functions of arbitrary order by the D-transformation

The D-transformation due to the author is an effective extrapolation method for computing infinite oscillatory integrals of various kinds. In this work two new variants of this transformation are designed for computing integrals of the form ∫a∞g(t)Cv(t)dt, where g(x) is a nonoscillatory function and Cv(x) may be an arbitrary linear combination of the Bessel functions of the first and second kinds Jv(x) and Yv(x), of arbitrary real order v. When applied to such integrals, the D-transformation and its new variants are observed to produce very accurate results. It is also seen that their performance is very similar to that of the modified W-transformation due to the author, as extended in a recent work by Lucas and Stone with Cv(x) = Jv(x). The present paper is concluded by stating the relevant convergence and stability results and by appending a numerical example.