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Relation of the Böttcher Equation with the Parametrized Poisson Integral. / Kalnitskii, V. S.; Petrov, A. N.

в: Vestnik St. Petersburg University: Mathematics, Том 51, № 4, 01.10.2018, стр. 373-379.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Kalnitskii, VS & Petrov, AN 2018, 'Relation of the Böttcher Equation with the Parametrized Poisson Integral', Vestnik St. Petersburg University: Mathematics, Том. 51, № 4, стр. 373-379. https://doi.org/10.3103/S106345411804009X

APA

Kalnitskii, V. S., & Petrov, A. N. (2018). Relation of the Böttcher Equation with the Parametrized Poisson Integral. Vestnik St. Petersburg University: Mathematics, 51(4), 373-379. https://doi.org/10.3103/S106345411804009X

Vancouver

Kalnitskii VS, Petrov AN. Relation of the Böttcher Equation with the Parametrized Poisson Integral. Vestnik St. Petersburg University: Mathematics. 2018 Окт. 1;51(4):373-379. https://doi.org/10.3103/S106345411804009X

Author

Kalnitskii, V. S. ; Petrov, A. N. / Relation of the Böttcher Equation with the Parametrized Poisson Integral. в: Vestnik St. Petersburg University: Mathematics. 2018 ; Том 51, № 4. стр. 373-379.

BibTeX

@article{e7a28586231b49b999d97e2cd79854e1,
title = "Relation of the B{\"o}ttcher Equation with the Parametrized Poisson Integral",
abstract = "The B{\"o}ttcher functional equation and one of its real generalizations are considered. It is shown that, in some situations, after finding a solution of the generalized equation, other solutions can also be obtained. For example, a three-parameter family of real functional equations for a function of two arguments is described, for which solutions are found. The generalization described has wide application. Many quantities after an appropriately introduced parameterization satisfy the generalized B{\"o}ttcher equation as functions of parameters. As an illustration, two-parametric families generated by the determinant of a linear combination of second-order matrices are presented. It is shown that the parameterized Poisson integral as a function of its parameters satisfies the generalized B{\"o}ttcher equation. This made it possible to calculate the Poisson integral and the Euler integral in a new way. In addition, the calculation of the Poisson integral by the method of integral sums is described.",
keywords = "B{\"o}ttcher equation, Poisson integral",
author = "Kalnitskii, {V. S.} and Petrov, {A. N.}",
note = "Publisher Copyright: {\textcopyright} 2018, Pleiades Publishing, Ltd. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.",
year = "2018",
month = oct,
day = "1",
doi = "10.3103/S106345411804009X",
language = "English",
volume = "51",
pages = "373--379",
journal = "Vestnik St. Petersburg University: Mathematics",
issn = "1063-4541",
publisher = "Pleiades Publishing",
number = "4",

}

RIS

TY - JOUR

T1 - Relation of the Böttcher Equation with the Parametrized Poisson Integral

AU - Kalnitskii, V. S.

AU - Petrov, A. N.

N1 - Publisher Copyright: © 2018, Pleiades Publishing, Ltd. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2018/10/1

Y1 - 2018/10/1

N2 - The Böttcher functional equation and one of its real generalizations are considered. It is shown that, in some situations, after finding a solution of the generalized equation, other solutions can also be obtained. For example, a three-parameter family of real functional equations for a function of two arguments is described, for which solutions are found. The generalization described has wide application. Many quantities after an appropriately introduced parameterization satisfy the generalized Böttcher equation as functions of parameters. As an illustration, two-parametric families generated by the determinant of a linear combination of second-order matrices are presented. It is shown that the parameterized Poisson integral as a function of its parameters satisfies the generalized Böttcher equation. This made it possible to calculate the Poisson integral and the Euler integral in a new way. In addition, the calculation of the Poisson integral by the method of integral sums is described.

AB - The Böttcher functional equation and one of its real generalizations are considered. It is shown that, in some situations, after finding a solution of the generalized equation, other solutions can also be obtained. For example, a three-parameter family of real functional equations for a function of two arguments is described, for which solutions are found. The generalization described has wide application. Many quantities after an appropriately introduced parameterization satisfy the generalized Böttcher equation as functions of parameters. As an illustration, two-parametric families generated by the determinant of a linear combination of second-order matrices are presented. It is shown that the parameterized Poisson integral as a function of its parameters satisfies the generalized Böttcher equation. This made it possible to calculate the Poisson integral and the Euler integral in a new way. In addition, the calculation of the Poisson integral by the method of integral sums is described.

KW - Böttcher equation

KW - Poisson integral

UR - http://www.scopus.com/inward/record.url?scp=85061204890&partnerID=8YFLogxK

U2 - 10.3103/S106345411804009X

DO - 10.3103/S106345411804009X

M3 - Article

AN - SCOPUS:85061204890

VL - 51

SP - 373

EP - 379

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 4

ER -

ID: 73360260