BLASCHKE, Petr a František ŠTAMPACH. The asymptotic zero distribution of Lommel polynomials as functions of their order with a variable complex argument. Journal of Mathematical Analysis and Applications. San Diego (USA): Academic Press Inc. Elsevier Science, 2020, roč. 490, č. 1, s. "124238-1"-"124238-19", 19 s. ISSN 0022-247X. Dostupné z: https://dx.doi.org/10.1016/j.jmaa.2020.124238. |
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@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 a 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, 2020, roč.~490, č.~1, s.~''124238-1''-''124238-19'', 19 s. ISSN~0022-247X. Dostupné z: https://dx.doi.org/10.1016/j.jmaa.2020.124238.
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