Bounded nonvanishing functions and bateman functions
Titel:
Bounded nonvanishing functions and bateman functions
Auteur:
Koepf, Wolfram Schmersau, Dieter
Verschenen in:
Complex variables and elliptic equations
Paginering:
Jaargang 25 (1994) nr. 3 pagina's 237-259
Jaar:
1994-03
Inhoud:
We consider the family B of bounded nonvanishing analytic functions [image omitted] in the unit disk. The coefficient problem had been extensively investigated (see e.g. [2, 13, 14, 16-18, 20]), and it is known that [image omitted] for n = 1, 2, 3, and 4. That this inequality may hold for [image omitted] is known as the Krzyz conjecture. It turns out that for fΣ B with a0=e-1[image omitted] SO that the superordinate functions [image omitted] are of special interest. The corresponding coefficient functions Fk(t) had been independently considered by Bateman [3] who had introduced them with the aid of the integral representation [image omitted] . We study the Bateman functions and formulate properties that give insight in the coefficient problem
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