This study is an extension of the earlier discussion of probabilistic Bell polynomials, and it looks at the probabilistic versions of the new type degenerate Bell polynomials associated with the random variable U. Here, U is a random variable, and the neighborhood surrounding the origin defines the moment-generating function for it. Our goals for these numbers and polynomials are to establish certain identities and recurrence relations, give explicit expressions, and derive certain features. We expect to find out more about these polynomials in a probabilistic context and investigate possible uses for them through this research.

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Probabilistic New Type Degenerate Bell Polynomials of the Second Kind Associated with Random Variables

  • Azhar Iqbal,
  • Waseem Ahmad Khan,
  • Naeem Ahmad

摘要

This study is an extension of the earlier discussion of probabilistic Bell polynomials, and it looks at the probabilistic versions of the new type degenerate Bell polynomials associated with the random variable U. Here, U is a random variable, and the neighborhood surrounding the origin defines the moment-generating function for it. Our goals for these numbers and polynomials are to establish certain identities and recurrence relations, give explicit expressions, and derive certain features. We expect to find out more about these polynomials in a probabilistic context and investigate possible uses for them through this research.