On properties of the solutions of the Weber equation

Yu.S. Trukhan

doi:10.15330/cmp.7.2.247-253

On properties of the solutions of the Weber equation

Authors

Yu.S. Trukhan Ivan Franko Lviv National University, 1 Universytetska str., 79000, Lviv, Ukraine

https://doi.org/10.15330/cmp.7.2.247-253

Keywords:

entire function,

$l$ -index boundedness, convex function, growth, Weber equation

Published online: 2015-12-24

Abstract

Growth, convexity and the $l$ -index boundedness of the functions $\alpha(z)$ and $\beta(z)$ , such that $\alpha(z^4)$ and $z\beta(z^4)$ are linear independent solutions of the Weber equation $w''-(\frac{z^2}4-\nu-\frac12) w=0$ if $\nu=-\frac12$ are investigated.