Probabilistic Bernoulli and Euler Polynomials

Let be a random variable whose moment generating function exists in a neighborhood of the origin. The aim of this paper is to introduce and study the probabilistic extension of Bernoulli polynomials and Euler polynomials, namely the probabilistic Bernoulli polynomials associated and the probabilisti...

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Bibliographic Details
Published inRussian journal of mathematical physics Vol. 31; no. 1; pp. 94 - 105
Main Authors Kim, T., Kim, D. S.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.03.2024
Springer Nature B.V
Subjects
14/34
639/766/189
639/766/530
639/766/747
Combinatorial analysis
Mathematical and Computational Physics
Parameters
Physics
Physics and Astronomy
Polynomials
Random variables
Statistical analysis
Theoretical
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Summary:Let be a random variable whose moment generating function exists in a neighborhood of the origin. The aim of this paper is to introduce and study the probabilistic extension of Bernoulli polynomials and Euler polynomials, namely the probabilistic Bernoulli polynomials associated and the probabilistic Euler polynomials associated with . Also, we introduce the probabilistic -Stirling numbers of the second associated , the probabilistic two variable Fubini polynomials associated , and the probabilistic poly-Bernoulli polynomials associated with . We obtain some properties, explicit expressions, certain identities and recurrence relations for those polynomials. As special cases of , we treat the gamma random variable with parameters , the Poisson random variable with parameter , and the Bernoulli random variable with probability of success . DOI 10.1134/S106192084010072
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1061-9208
1555-6638
DOI:10.1134/S106192084010072