Displaying similar documents to “On polynomial expansion of multivalent functions.”

Starlikeness of polynomials and finite Blaschke products

Alan Gluchoff, Frederick Hartmann (2008)

Annales Polonici Mathematici

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The radius of starlikeness for polynomial mappings and finite Blaschke products with zeroes distributed at equal angles around a circle centered at the origin, as well as with zeroes concentrated at a single point, are considered, and sharp bounds are obtained. Results expressing the radius of starlikeness of an arbitrary polynomial or Blaschke product in terms of the magnitudes of the zeroes are also given. These are also sharp.

Linearly-invariant families and generalized Meixner–Pollaczek polynomials

Iwona Naraniecka, Jan Szynal, Anna Tatarczak (2013)

Annales UMCS, Mathematica

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The extremal functions f0(z) realizing the maxima of some functionals (e.g. max |a3|, and max arg f′(z)) within the so-called universal linearly invariant family Uα (in the sense of Pommerenke [10]) have such a form that f′0(z) looks similar to generating function for Meixner-Pollaczek (MP) polynomials [2], [8]. This fact gives motivation for the definition and study of the generalized Meixner-Pollaczek (GMP) polynomials Pλn (x; θ,ψ) of a real variable x as coefficients of [###] where...

An extension of typically-real functions and associated orthogonal polynomials

Iwona Naraniecka, Jan Szynal, Anna Tatarczak (2011)

Annales UMCS, Mathematica

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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...

An extension of typically-real functions and associated orthogonal polynomials

Iwona Naraniecka, Jan Szynal, Anna Tatarczak (2011)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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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...