id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-5702	Lee, Si Hyeon; Chen li	Probabilistic Multiple poly Bernoulli Polynomials of the Second kind	2025	13	.pdf	application/pdf	4247	312	88	In section 2, we define probabilistic poly Bernoulli polynomials of the second kind b (k) n,Y and probabilistic multiple poly Bernoulli polynomials of the second kind b (k1,...,kr) n,Y associated with Y . (18) 2. probabilistic poly and multiple poly Bernoulli polynomials of the second kind In this section, we consider probabilistic poly Bernoulli polynomials of the second kind associated with Y which are given by Lik(1− E[e−Y t]) log(1 + t) (1 + t)x = ∞∑ n=0 b (k) n,Y (x) tn n! .	cache/ejpam-5702.pdf	txt/ejpam-5702.txt