Unification of Two-Variable Family of Apostol-Type Polynomials with Applications

Unification of Two-Variable Family of Apostol-Type Polynomials with Applications

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In this paper, the two-variable unified family of ventilationstejp generalized Apostol-type polynomials is introduced, and some implicit forms and general symmetry identities are derived.Also, we obtain new degenerate Apostol-type numbers and polynomials constructed from the new 2-variable unified family.We derive explicit formulae of polynomials and identities that include some special numbers and polynomials.In addition, a probabilistic arrethe bush balm representation of the new family and some statistical properties are obtained.