Unified degenerate Apostol-type Bernoulli, Euler, Genocchi, and Fubini polynomials

Abstract

[10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] introduced and investigated the Apostol-type Bernoulli, Euler, Genocchi and Fubini polynomials. Acala gave some identities and symmetric relations for those polynomials. In this paper, we define the unified degenerate Apostol-type Bernoulli, Euler, Genocchi, and Fubini polynomials. We give identities and recurrence relations, symmetric relation, and summation formulas.

Generalized Fubini Apostol-Type Polynomials and Probabilistic Applications

“…Unified degenerate aApostol-type Bernoulli, Euler, Genocchi, and Fubini polynomials [24] 8 y � − 1, j � 1 and ψ(t, α i ) � (α i b t − 2a t ) in ( 19)…”

A note on partially degenerate Hermite-Bernoulli polynomials of the first kind

“…From (1.14) and (1.15), we note that the generating function of Stirling numbers of the first kind and that of the second kind are respectively given by (see [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]):…”