View in EDS HTML Full Text PDF Full Text

Probabilistic degenerate Bernstein polynomials.

Saved in:
Bibliographic Details
Title: Probabilistic degenerate Bernstein polynomials.
Authors: Wang, Jinyu1 (AUTHOR), Ma, Yuankui1 (AUTHOR) mayuankui@xatu.edu.cn, Kim, Taekyun1,2 (AUTHOR) tkkim@kw.ac.kr, Kim, Dae San3 (AUTHOR) dskim@sogang.ac.kr
Source: Applied Mathematics in Science & Engineering. Dec2025, Vol. 33 Issue 1, p1-15. 15p.
Subjects: Bernstein polynomials, Random variables, Stochastic processes, Polynomials, Poisson distribution, Characteristic functions, Binomial distribution, Binomial theorem
Abstract: In recent years, both degenerate versions and probabilistic extensions of many special numbers and polynomials have been explored. For instance, degenerate Bernstein polynomials and probabilistic Bernstein polynomials were investigated earlier. Assume that Y is a random variable whose moment generating function exists in a neighbourhood of the origin. The aim of this paper is to study probabilistic degenerate Bernstein polynomials associated with Y which are both probabilistic extension of the degenerate Bernstein polynomials and degenerate version of the probabilistic Bernstein polynomials associated with Y. We derive several explicit expressions and certain related identities for those polynomials. In addition, we treat the special cases of the Poisson random variable, the Bernoulli random variable and of the binomial random variable. [ABSTRACT FROM AUTHOR]
Copyright of Applied Mathematics in Science & Engineering is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
Full text is not displayed to guests.
FullText Links:
  – Type: pdflink
Text:
  Availability: 1
Header DbId: egs
DbLabel: Engineering Source
An: 190352364
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Probabilistic degenerate Bernstein polynomials.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Wang%2C+Jinyu%22">Wang, Jinyu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Ma%2C+Yuankui%22">Ma, Yuankui</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> mayuankui@xatu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Kim%2C+Taekyun%22">Kim, Taekyun</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> tkkim@kw.ac.kr</i><br /><searchLink fieldCode="AR" term="%22Kim%2C+Dae+San%22">Kim, Dae San</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> dskim@sogang.ac.kr</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Applied+Mathematics+in+Science+%26+Engineering%22">Applied Mathematics in Science & Engineering</searchLink>. Dec2025, Vol. 33 Issue 1, p1-15. 15p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Bernstein+polynomials%22">Bernstein polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Random+variables%22">Random variables</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+processes%22">Stochastic processes</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomials%22">Polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Poisson+distribution%22">Poisson distribution</searchLink><br /><searchLink fieldCode="DE" term="%22Characteristic+functions%22">Characteristic functions</searchLink><br /><searchLink fieldCode="DE" term="%22Binomial+distribution%22">Binomial distribution</searchLink><br /><searchLink fieldCode="DE" term="%22Binomial+theorem%22">Binomial theorem</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: In recent years, both degenerate versions and probabilistic extensions of many special numbers and polynomials have been explored. For instance, degenerate Bernstein polynomials and probabilistic Bernstein polynomials were investigated earlier. Assume that Y is a random variable whose moment generating function exists in a neighbourhood of the origin. The aim of this paper is to study probabilistic degenerate Bernstein polynomials associated with Y which are both probabilistic extension of the degenerate Bernstein polynomials and degenerate version of the probabilistic Bernstein polynomials associated with Y. We derive several explicit expressions and certain related identities for those polynomials. In addition, we treat the special cases of the Poisson random variable, the Bernoulli random variable and of the binomial random variable. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Applied Mathematics in Science & Engineering is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=190352364
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1080/27690911.2024.2448191
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 15
        StartPage: 1
    Subjects:
      – SubjectFull: Bernstein polynomials
        Type: general
      – SubjectFull: Random variables
        Type: general
      – SubjectFull: Stochastic processes
        Type: general
      – SubjectFull: Polynomials
        Type: general
      – SubjectFull: Poisson distribution
        Type: general
      – SubjectFull: Characteristic functions
        Type: general
      – SubjectFull: Binomial distribution
        Type: general
      – SubjectFull: Binomial theorem
        Type: general
    Titles:
      – TitleFull: Probabilistic degenerate Bernstein polynomials.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Wang, Jinyu
      – PersonEntity:
          Name:
            NameFull: Ma, Yuankui
      – PersonEntity:
          Name:
            NameFull: Kim, Taekyun
      – PersonEntity:
          Name:
            NameFull: Kim, Dae San
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 12
              Text: Dec2025
              Type: published
              Y: 2025
          Identifiers:
            – Type: issn-print
              Value: 27690911
          Numbering:
            – Type: volume
              Value: 33
            – Type: issue
              Value: 1
          Titles:
            – TitleFull: Applied Mathematics in Science & Engineering
              Type: main
ResultId 1