Properties of the solutions of the Gauss equation 

Author 
yurik93@mail.ru
Ivan Franko National University of Lviv

Abstract 
It is proved that the Gauss equation $z(z1)w''+((\alpha+\beta+1)z\gamma)w'+\alpha\beta w=0$
apart from the hypergeometric function has a power solution
with negative exponents. Its possible growth, closetoconvexity and $l$index boundedness are investigated.

Keywords 
Gauss equation; hypergeometric function; closetoconvexity; $l$index boundedness

Reference 
1. Golusin G.M., Geometric theory of functions of a complex variable. – American Math. Soc., 1966. – 676 p.
2. Sheremeta M.M., Analytic functions of bounded index. – Lviv: VNTL Publishers, 1999. – 141 p. 3. Kuznetsov D.S., Special functions. – M.: Vysshaya Shkola, 1965. – 423 p. (in Russian) 4. Sheremeta M.M. Properties of the hypergeometric function with positive parameters// Visnyk Lviv Univ., Ser. Mech. Math. – 2009. – V.70. – P. 183–190. (in Ukrainian) 5. Juneja O.P., Reddy T.R. Meromorphic starlike and univalent functions with positive coefficients// Ann. Univ. Mariae CurieSklodowska. – 1985. – V.39. – P. 65–76. 6. Mogra M.L. Hadamard product certain meromorphic univalent functions// J. Math. Anal. Appl. – 1991. – V.157. – P. 10–16. 7. Goodman A.W., Univalent function. – V.II, Mariner Publishing Co., 1983. – 158 p. 
Pages 
157167

Volume 
41

Issue 
2

Year 
2014

Journal 
Matematychni Studii

Full text of paper  
Table of content of issue 