(Springer US, 2018) López García, José Luis; Pagola Martínez, Pedro Jesús; Matematika eta Informatika Ingeniaritza; Institute for Advanced Materials and Mathematics - INAMAT2; Ingeniería Matemática e Informática; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
We consider the Bessel functions Jν (z) and Yν (z) for ν > −1/2 and
z ≥ 0. We derive a convergent expansion of Jν (z) in terms of the derivatives of
(sin z)/z, and a convergent expansion of Yν (z) in terms of derivatives of (1−cos z)/z,
derivatives of (1 − e−z)/z and (2ν, z). Both expansions hold uniformly in z in any
fixed horizontal strip and are accompanied by error bounds. The accuracy of the
approximations is illustrated with some numerical experiments.