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1. CJM 2010 (vol 62 pp. 261)
Erratum to: On Value Distribution Theory of Second Order Periodic ODEs, Special Functions and Orthogonal Polynomials |
Erratum to: On Value Distribution Theory of Second Order Periodic ODEs, Special Functions and Orthogonal Polynomials No abstract.
Keywords:Complex Oscillation theory, Exponent of convergence of zeros, zero distribution of Bessel and Confluent hypergeometric functions, Lommel transform, Bessel polynomials, Heine Problem Categories:34M10, 33C15, 33C47 |
2. CJM 2009 (vol 61 pp. 373)
An Infinite Order Whittaker Function In this paper we construct a flat smooth section of an induced space
$I(s,\eta)$ of $SL_2(\mathbb{R})$ so that the attached Whittaker function
is not of finite order.
An asymptotic method of classical analysis is used.
Categories:11F70, 22E45, 41A60, 11M99, 30D15, 33C15 |
3. CJM 2006 (vol 58 pp. 726)
On Value Distribution Theory of Second Order Periodic ODEs, Special Functions and Orthogonal Polynomials |
On Value Distribution Theory of Second Order Periodic ODEs, Special Functions and Orthogonal Polynomials We show that the value distribution (complex oscillation) of
solutions of certain periodic second order ordinary differential
equations studied by Bank, Laine and Langley is closely
related to confluent hypergeometric functions, Bessel functions
and Bessel polynomials. As a result, we give a complete
characterization of the zero-distribution in the sense of
Nevanlinna theory of the solutions for two classes of the ODEs.
Our approach uses special functions and their asymptotics. New
results concerning finiteness of the number of zeros
(finite-zeros) problem of Bessel and Coulomb wave functions with
respect to the parameters are also obtained as a consequence. We
demonstrate that the problem for the remaining class of ODEs not
covered by the above ``special function approach" can be
described by a classical Heine problem for differential
equations that admit polynomial solutions.
Keywords:Complex Oscillation theory, Exponent of convergence of zeros, zero distribution of Bessel and Confluent hypergeometric functions, Lommel transform, Bessel polynomials, Heine Proble Categories:34M10, 33C15, 33C47 |