@article{Katkova_Lobova-Eisner_Vishnyakova_2004, place={Харків, Україна}, title={On entire functions having Taylor sections with only real zeros}, volume={11}, url={http://mag.ilt.kharkiv.ua/index.php/mag/article/view/m11-0449e}, abstractNote={We investigate power series with positive coefficients having sections with only real zeros. For an entire function f(z) =∑∞k=0akzk, ak > 0; we denote by qn(f) :=(a2n-1)/(an-2an) n ≥ 2. The following problem remains open:
which entire function with positive coefficients and sections with only real zeros has the minimal possible lim infn→∞ qn(f)? We prove that the ex-
tremal function in the class of such entire functions with additional condi
tion $ lim n→∞ qn(f) is the function of the form fa(z) := ∑∞k=0(zk)/k! ak2. We
answer also the following questions: for which a do the function fa(z) and the function ya(z) := 1+∑∞k=1(zk)/((ak-1)(ak-1-1)...(a-1)), a>1, have sections with only real zeros?}, number={4}, journal={Математическая физика, анализ, геометрия}, author={Katkova, Olga M. and Lobova-Eisner, Tatjana and Vishnyakova, Anna M.}, year={2004}, month={Трав}, pages={449–469} }