title: Connection of the B¨ottcher equation with the parametrized Poisson integral
metadata.name: dc.contributor.author
metadata.value: Kalnitsky, Vyacheslav S.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Petrov, Andrey N.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-12-13T14:32:58Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-12-13T14:32:58Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Kalnitsky V. S., Petrov A.N. Connection of the B¨ottcher equation with the parametrized Poisson integral. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 4, pp. 614–622.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.407
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/15129
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In the paper, one of the real generalizations of the B¨ottcher equation is considered. It
  is shown that in some situations, after finding the particular solution of the generalized equation, it is possible to obtain other solutions of it. As an example, we describe a threeparameter
  family of real functional equations for a function of two arguments, for which
  particular solutions are found. This generalization has a wide field of application. Many
  quantities after a properly introduced parametrization satisfy the generalized B¨ottcher
  equation as a function of the parameters. As an illustration, we give two-parameter families
  generated by the determinant of a linear combination of second-order matrices. It is
  shown that the parametrized Poisson integral, as a function of its parameters, satisfies the
  generalized B¨ottcher equation. This allowed us to calculate the Poisson integral and the
  Euler integral in a new way. As a supplement, the calculation of the Poisson integral by
  the method of integral sums is presented.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 5 (63); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: B¨ottcher equation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Poisson integral
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Connection of the B¨ottcher equation with the parametrized Poisson integral
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 07-Kalnitskiy.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/15129/1/07-Kalnitskiy.pdf
resources.format: Adobe PDF
resources.size: 272,39 kB