Erratum to: On Value Distribution Theory of Second Order Periodic ODEs, Special Functions and Orthogonal Polynomials

2010 ◽  
Vol 62 (2) ◽  
pp. 261-261
Author(s):  
Yik-Man Chiang ◽  
Mourad E. H. Ismail
Keyword(s):  
Orthogonal Polynomials ◽  
Special Functions ◽  
Distribution Theory ◽  
Second Order ◽  
Value Distribution ◽  
Value Distribution Theory

scholarly journals On Value Distribution Theory of Second Order Periodic ODEs, Special Functions and Orthogonal Polynomials

2006 ◽  
Vol 58 (4) ◽  
pp. 726-767 ◽  
Author(s):  
Yik-Man Chiang ◽  
Mourad E. H. Ismail
Keyword(s):  
Differential Equations ◽  
Special Functions ◽  
Complete Characterization ◽  
Second Order ◽  
Value Distribution ◽  
Value Distribution Theory ◽  
Confluent Hypergeometric Functions ◽  
Number Of Zeros ◽  
Oscillation Of Solutions

AbstractWe 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.

Sign in / Sign up

Export Citation Format

Share Document