title: Estimates of sums of integrals of Legendre polynomial
metadata.name: dc.contributor.author
metadata.value: Kholshevnikov, Konstantin V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Shaidulin, Vakhit Sh.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2016-08-01T11:04:50Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2016-08-01T11:04:50Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2016-06
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/2461
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Estimates of sums
  Rnk(x) =
  ∞ 
  m=n
  Pmk(x) are established. Here
  Pn0(x) = Pn(x), Pnk(x) =
   x
  −1
  Pn,k−1(y)dy,
  Pn being a Legendre polynomial with the standard normalisation Pn(1) = 1. If k = 1 then the sum
  decreases with growing n as n−1 if x belongs to the main segment [−1, 1], wheras it decreases as n−3/2
  if x belongs to the semi-segment [−1, 1). If k > 1 the point x = 1 does not need to be excluded. The sum
  decreases as n−k−1/2. The more, a small increasing of the multiplicative constant permits to obtain an
  estimate
  |Rnk(cos θ)| <
  C sink−3/2 θ
  nk+1/2,
  where C depends weakly on k (but not on n, θ). As a by-product, the integral of Mehler—Dirichlet type
  for Rnk(cos θ) is deduced. Refs 6. Figs 3. Tables 1.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при финансовой поддержке РФФИ (грант 14-02-00804) и СПбГУ (грант
  6.37.341.2015).
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. Series 1. Mathematics. Mechanics. Astronomy;Vol. 3 (61); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: Legendre polynomials
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: estimate of sums
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: estimate of a remainder of a series
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Estimates of sums of integrals of Legendre polynomial
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
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