I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2002, VOLUME 8, NUMBER 4, PAGES 1159-1178
Zeroes of Schrödinger's radial function
and Kummer's function
V. F. Tarasov
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Exact formulae for calculation of zeroes of Kummer's polynomials at
are given; in other cases () their numerical
values (to within ) are given.
It is shown that the methods of L. Ferrari, L. Euler and
J.-L. Lagrange that are used for solving the equation
are based on one (common for all methods) equation of
cubic resolvent of FEL-type.
For greater geometrical clarity of (nonuniform for ) distribution of
on the axis
the "circular" diagrams with the radius
are introduced for the first time.
It allows to notice some singularities of distribution of these zeroes
and their "images", i. e.
the points on the circle.
Exact "angle" asymptotics of the points for
While calculating zeroes of the
functions, the "singular" cases are found.
All articles are
published in Russian.
Last modified: April 10, 2003