Probabilistic Bernoulli and Euler Polynomials

Kim, T.; Kim, D. S.

doi:10.1134/s106192084010072

Russ. J. Math. Phys.

2024

DOI: 10.1134/s106192084010072

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Probabilistic Bernoulli and Euler Polynomials

T. Kim,

D. S. Kim

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Cited by 14 publications

References 16 publications

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Probabilistic degenerate Stirling numbers of the first kind and their applications

Kim,

Kim

2024

European Journal of Mathematics

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Probabilistic degenerate Stirling numbers of the first kind and their applications

Kim,

Kim

2024

European Journal of Mathematics

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Probabilistic Degenerate Fubini Polynomials Associated with Random Variables

Xu,

Kim,

Kim

et al. 2024

J Nonlinear Math Phys

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Let Y be a random variable such that the moment generating function of Y exists in a neighborhood of the origin. The aim of this paper is to study probabilistic versions of the degenerate Fubini polynomials and the degenerate Fubini polynomials of order r, namely the probabilisitc degenerate Fubini polynomials associated with Y and the probabilistic degenerate Fubini polynomials of order r associated with Y. We derive some properties, explicit expressions, certain identities and recurrence relations for those polynomials. As special cases of Y, we treat the gamma random variable with parameters $$\alpha ,\beta > 0$$ α , β > 0 , the Poisson random variable with parameter $$\alpha > 0$$ α > 0 , and the Bernoulli random variable with probability of success p.

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A probabilistic proof of some integral formulas involving incomplete gamma functions

Gaunt

2024

Communications in Statistics - Theory and Methods

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Probabilistic Bernoulli and Euler Polynomials

Cited by 14 publications

References 16 publications

Probabilistic degenerate Stirling numbers of the first kind and their applications

Probabilistic degenerate Stirling numbers of the first kind and their applications

Probabilistic Degenerate Fubini Polynomials Associated with Random Variables

A probabilistic proof of some integral formulas involving incomplete gamma functions

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