Generalized Typically Real Functions

Stanislawa Kanas, Anna Tatarczak


Let $f(z) = z+a_2 z^2+\cdots$ be regular in the
unit diskĀ  and real valued if and only if $z$ is real and $|z| < 1$.
Then $f$ is said to be typically real function. Rogosinski found
the necessary and sufficient condition for a regular function to be
typically-real. The main purpose of the presented paper is a
consideration of the generalized typically-real functions defined
via the generating function of the generalized Chebyshev polynomials
of the second kind
U_n(p,q;e^{i\theta})z^n, $$ where $-1\le p,q \le 1, \ \theta \in
\langle 0,2\pi\rangle, \ |z|<1.$

Full Text:



  • There are currently no refbacks.