An extension of typically-real functions and associated orthogonal polynomials

Iwona Naraniecka, Jan Szynal, Anna Tatarczak

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.


Keywords


Typically-real functions; univalent functions; local univalence; univalence; starlikeness; Chebyshev polynomials; orthogonal polynomials

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References


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DOI: http://dx.doi.org/10.2478/v10062-011-0017-2
Date of publication: 2016-07-27 21:54:10
Date of submission: 2016-07-26 21:50:50


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