A family of Apostol–Euler polynomials associated with Bell polynomials

Many authors investigated the characteristics of the Bell, Euler, Bernoulli, and Genocchi polynomials because of their numerous uses in statistics, number theory, and other branches of science. A generating function for mixed-type Apostol–Euler polynomials of order η related with Bell polynomials is...

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Bibliographic Details
Published inAnalysis (Wiesbaden) Vol. 44; no. 1; pp. 1 - 16
Main Authors Khan, Nabiullah, Husain, Saddam
Format Journal Article
LanguageEnglish
Published De Gruyter Oldenbourg 01.02.2024
Subjects
11B68
33B15
33C05
33C10
33C15
33C45
33E20
Bell polynomial
Euler polynomials
Stirling number of second kind
Stirling polynomial
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Summary:Many authors investigated the characteristics of the Bell, Euler, Bernoulli, and Genocchi polynomials because of their numerous uses in statistics, number theory, and other branches of science. A generating function for mixed-type Apostol–Euler polynomials of order η related with Bell polynomials is presented in this study. We also construct essential identities of Apostol–Euler polynomials of order η connected with Bell polynomials, such as the correlation formula, the implicit summation formula, the derivative formula, some association with Stirling numbers, and specific cases. Also we establish certain symmetric identities and their known consequences. In addition, we investigate several interesting relationships related to umbral calculus.
ISSN:0174-4747
2196-6753
DOI:10.1515/anly-2022-1101