On the zeros of <script type="math/tex">J_{n}(z)\pm iJ_{n+1}(z)</script> and <script type="math/tex">[J_{n+1}(z)]^{2}-J_{n}(z)J_{n+2}(z)</script>

Kravanja, Peter; Verlinden, Pierre

doi:10.1016/S0377-0427(00)00315-0

Title

On the zeros of $J_{n}(z)\pm iJ_{n+1}(z)$ and $[J_{n+1}(z)]^{2}-J_{n}(z)J_{n+2}(z)$

Author

Kravanja, Peter

Verlinden, Pierre

Abstract

The zeros of Jn(z) ± i Jn+1(z) and [Jn+1(z)]2 − Jn(z)Jn+2(z) play an important role in certain physical applications.At the origin these functions have a zero of multiplicity n (if n¿1) and 2n+2, respectively.We prove that all the zeros that lie in C0 are simple. ZEBEC (Kravanja et al., Comput.Phys.Commun.113(23) (1998) 220238) is a reliable software package for calculating zeros of Bessel functions of the :rst, the second, or the third kind, or their :rst derivatives.It can be easily extended to calculate zeros of any analytic function, provided that the zeros are known to be simple.Thus, ZEBEC is the package of choice to calculate the zeros of Jn(z)±i Jn+1(z) or [Jn+1(z)]2−Jn(z)Jn+2(z).We tabulate the :rst 30 zeros of J5(z) − i J6(z) and J10(z) − i J11(z) that lie in the fourth quadrant as computed by ZEBEC.

Language

English

Source (journal)

Journal of computational and applied mathematics. - Antwerp, 1975, currens

Publication

Antwerp : 2001

ISSN

0377-0427 [print]

1879-1778 [online]

DOI

10.1016/S0377-0427(00)00315-0

Volume/pages