An extension of typically-real functions and associated orthogonal polynomials
Iwona Naraniecka; Jan Szynal; Anna Tatarczak
Annales UMCS, Mathematica (2011)
- Volume: 65, Issue: 2, page 99-112
- ISSN: 2083-7402
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topIwona Naraniecka, Jan Szynal, and Anna Tatarczak. "An extension of typically-real functions and associated orthogonal polynomials." Annales UMCS, Mathematica 65.2 (2011): 99-112. <http://eudml.org/doc/268336>.
@article{IwonaNaraniecka2011,
abstract = {Two-parameters extension of the family of typically-real functions is studied. The definition is obtained by the Stjeltjes integral formula. The kernel function in this definition serves as a generating function for some family of orthogonal polynomials generalizing Chebyshev polynomials of the second kind. The results of this paper concern the exact region of local univalence, bounds for the radius of univalence, the coefficient problems within the considered family as well as the basic properties of obtained orthogonal polynomials.},
author = {Iwona Naraniecka, Jan Szynal, Anna Tatarczak},
journal = {Annales UMCS, Mathematica},
keywords = {Typically-real functions; univalent functions; local univalence; univalence; starlikeness; Chebyshev polynomials; orthogonal polynomials; typically-real functions},
language = {eng},
number = {2},
pages = {99-112},
title = {An extension of typically-real functions and associated orthogonal polynomials},
url = {http://eudml.org/doc/268336},
volume = {65},
year = {2011},
}
TY - JOUR
AU - Iwona Naraniecka
AU - Jan Szynal
AU - Anna Tatarczak
TI - An extension of typically-real functions and associated orthogonal polynomials
JO - Annales UMCS, Mathematica
PY - 2011
VL - 65
IS - 2
SP - 99
EP - 112
AB - Two-parameters extension of the family of typically-real functions is studied. The definition is obtained by the Stjeltjes integral formula. The kernel function in this definition serves as a generating function for some family of orthogonal polynomials generalizing Chebyshev polynomials of the second kind. The results of this paper concern the exact region of local univalence, bounds for the radius of univalence, the coefficient problems within the considered family as well as the basic properties of obtained orthogonal polynomials.
LA - eng
KW - Typically-real functions; univalent functions; local univalence; univalence; starlikeness; Chebyshev polynomials; orthogonal polynomials; typically-real functions
UR - http://eudml.org/doc/268336
ER -
References
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