Properties of the solutions of the Gauss equation

Author
M. M. Sheremeta, Yu. S. Trukhan
Ivan Franko National University of Lviv
Abstract
It is proved that the Gauss equation $z(z-1)w''+((\alpha+\beta+1)z-\gamma)w'+\alpha\beta w=0$ apart from the hypergeometric function has a power solution with negative exponents. Its possible growth, close-to-convexity and $l$-index boundedness are investigated.
Keywords
Gauss equation; hypergeometric function; close-to-convexity; $l$-index boundedness
Reference
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Pages
157-167
Volume
41
Issue
2
Year
2014
Journal
Matematychni Studii
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