Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0561.65011
Kerimov, M.K.; Skorokhodov, S.L.
On the computation of the complex zeros of the Bessel functions $J\sb{\nu}(z)$ and $I\sb{\nu}(z)$ and their derivatives. (Russian)
[J] Zh. Vychisl. Mat. Mat. Fiz. 24, No.10, 1497-1513 (1984). ISSN 0044-4669

The authors compute complex zeros of $J\sb{\nu}(z)$, $I\sb{\nu}(z)$ and their derivatives, where $\nu$ is real. It is known that if $\nu >-1$, then $J\sb{\nu}(z)$ has only real zeros, while if $\nu <-1$, and $\nu$ is not an integer, then $J\sb{\nu}(z)$ has $2\lfloor -\nu \rfloor$ complex zeros. The method is due to Newton iteration, starting from an asymptotic formula giving the approximate zeros. They give the table of complex zeros of $I\sb{\nu}(z)$ for $\nu =1.5(1)20.5$ and of $I'\sb{\nu}(z)$ for $\nu =0.5(1)20.5$. Further they consider the double zero of $J\sb{\nu}(z)$. According to the Bessel's differential equation, $J'\sb{\nu}(z\sb 0) = J''\sb{\nu}(z\sb 0) = 0$ may occur only at $z\sb0 = \mp\nu$, $\nu<0$. They give first 100 values of such $\nu$'s. The difference of contiguous two values tends to 1.
[S.Hitotumatu]

MSC 2000:: *65D20 Computation of special functions
65H05 Single nonlinear equations (numerical methods)
33C10 Cylinder functions, etc.

Keywords: complex zero of Bessel functions; derivative of Bessel functions; Newton iteration; asymptotic formula

Cited in: Zbl 0614.65055 Zbl 0603.65029 Zbl 0582.65012

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]