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A Probabilistic Extension of the Fubini Polynomials

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Abstract

In this paper, we present a probabilistic extension of the Fubini polynomials and numbers associated with a random variable satisfying some appropriate moment conditions. We obtain the exponential generating function and an integral representation for it. The higher order Fubini polynomials and recurrence relations are also derived. A probabilistic generalization of a series transformation formula and some interesting examples are discussed. A connection between the probabilistic Fubini polynomials and Bernoulli, Poisson, and geometric random variables are also established. Finally, a determinant expression formula is presented.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Central University of Punjab, Bathinda, Punjab, 151401, India

    R. Soni & A. K. Pathak

  2. Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India

    P. Vellaisamy

Authors
  1. R. Soni
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  2. A. K. Pathak
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  3. P. Vellaisamy
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All authors contributed equally in this paper.

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Correspondence to A. K. Pathak.

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Communicated by Rosihan M. Ali.

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The research of R. Soni was supported by CSIR (File No: 09/1051(11349)/2021-EMR-I), Government of India. A. K. Pathak would like to express his gratitude to Science and Engineering Research Board (SERB), India for financial support under the MATRICS research grant MTR/2022/000796.

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Soni, R., Pathak, A.K. & Vellaisamy, P. A Probabilistic Extension of the Fubini Polynomials. Bull. Malays. Math. Sci. Soc. 47, 102 (2024). https://doi.org/10.1007/s40840-024-01702-7

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  • DOI: https://doi.org/10.1007/s40840-024-01702-7

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