The asymptotic zero distribution of Lommel polynomials as functions of their order with a variable ...

@article{49240,
   author = {Blaschke, Petr and Štampach, František},
   article_location = {San Diego (USA)},
   article_number = {1},
   doi = {http://dx.doi.org/10.1016/j.jmaa.2020.124238},
   keywords = {Lommel polynomials; Zeros; Asymptotic zero distribution; Variable parameters},
   language = {eng},
   issn = {0022-247X},
   journal = {Journal of Mathematical Analysis and Applications},
   title = {The asymptotic zero distribution of Lommel polynomials as functions of their order with a variable complex argument},
   url = {https://www.sciencedirect.com/science/article/pii/S0022247X20304005?via%3Dihub},
   volume = {490},
   year = {2020}
}

TY  - JOUR
ID  - 49240
AU  - Blaschke, Petr - Štampach, František
PY  - 2020
TI  - The asymptotic zero distribution of Lommel polynomials as functions of their order with a variable complex argument
JF  - Journal of Mathematical Analysis and Applications
VL  - 490
IS  - 1
SP  - "124238-1"-"124238-19"
EP  - "124238-1"-"124238-19"
PB  - Academic Press Inc. Elsevier Science
SN  - 0022247X
KW  - Lommel polynomials
KW  - Zeros
KW  - Asymptotic zero distribution
KW  - Variable parameters
UR  - https://www.sciencedirect.com/science/article/pii/S0022247X20304005?via%3Dihub
N2  - We study the asymptotic distribution of roots of Lommel polynomials as polynomials of the order with a variable and purely imaginary argument. The roots are complex and accumulate on certain curves in the complex plane. We prove existence of the weak limit of corresponding root-counting measures and deduce formulas for the supporting curves and density. The obtained result represents a solvable example of a more general problem which is still open. Numerical illustrations of the main result are also involved.
ER  - 

BLASCHKE, Petr and František ŠTAMPACH. The asymptotic zero distribution of Lommel polynomials as functions of their order with a variable complex argument. \textit{Journal of Mathematical Analysis and Applications}. San Diego (USA): Academic Press Inc. Elsevier Science, vol.~490, No~1, p.~''124238-1''-''124238-19'', 19 pp. ISSN~0022-247X. doi:10.1016/j.jmaa.2020.124238. 2020.