Title
On the zeros of <tex>$J_{n}(z)\pm iJ_{n+1}(z)$</tex> and <tex>$[J_{n+1}(z)]^{2}-J_{n}(z)J_{n+2}(z)$</tex> On the zeros of <tex>$J_{n}(z)\pm iJ_{n+1}(z)$</tex> and <tex>$[J_{n+1}(z)]^{2}-J_{n}(z)J_{n+2}(z)$</tex>
Author
Faculty/Department
Faculty of Social Sciences. Communication Sciences
Publication type
article
Publication
Antwerp ,
Subject
Computer. Automation
Source (journal)
Journal of computational and applied mathematics. - Antwerp
Volume/pages
132(2001) :2 , p. 237-245
ISSN
0377-0427
ISI
000169651500002
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
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.
E-info
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