A differentiation formula for spherical Bessel functions

doi:10.1088/0305-4470/38/8/005

A differentiation formula for spherical Bessel functions

J Boersma et al 2005 J. Phys. A: Math. Gen. 38 1687-1690 doi: 10.1088/0305-4470/38/8/005

PDF (57 KB) | References | Articles citing this article

J Boersma^1,3 and M L Glasser²
¹ Department of Mathematics and Computing Science, Eindhoven University of Technology, Eindhoven, The Netherlands
² Department of Physics and Center for Quantum Device Technology, Clarkson University, Potsdam, NY 13699-5820, USA
³ Professor Boersma passed away during the completion of this paper

Abstract. The differentiation formula $\fl \left(1-\frac{\sqrt{z^2+a^2}}{z} \frac{\rm d}{{\rm d}z}\right)^n [z^{n-1/2}K_{n-1/2}(z)] = \big(z+\sqrt{z^2+a^2}\big)^n z^{-1/2}K_{1/2}(z)$

is derived, where K_n−1/2(z) is a modified spherical Bessel function and a is an arbitrary constant.

PACS number: 02.30.Gp

Print publication: Issue 8 (25 February 2005)
Received 5 October 2004, in final form 23 November 2004
Published 9 February 2005

Post to CiteUlike |

Post to Connotea |

Post to Bibsonomy

A differentiation formula for spherical Bessel functions

Find related articles

Article options

Authors & Referees