Cover Image

Representations by probabilistic Bernoulli and degenerate Bernoulli polynomials

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Kim, Dae san, Kim, Taekyun
Format:	Preprint
Published:	2025
Subjects:	Number Theory Probability 05A19, 05A40, 11B68, 11B73, 11B83, 60-08
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Representations by probabilistic Frobenius-Euler and degenerate Frobenius-Euler polynomials
by: Kim, Taekyun, et al.
Published: (2025)

Probabilistic degenerate logarithm and heterogeneous stirling numbers
by: Kim, Dae San, et al.
Published: (2026)

Degenerate Sheffer-type polynomials and degenerate Sheffer polynomials associated with a random variable
by: Kim, Taekyun, et al.
Published: (2025)

Probabilistic degenerate Stirling numbers of the first kind and their applications
by: Kim, Taekyun, et al.
Published: (2024)

Probabilistic heterogeneous Stirling numbers and Bell polynomials
by: Kim, Taekyun, et al.
Published: (2026)

Probabilistic degenerate Bernstein polynomials
by: Wang, Jinyu, et al.
Published: (2024)

Probabilistic degenerate poly-Bell polynomials associated with random variables
by: Xue, Pengxiang, et al.
Published: (2025)

Probabilistic generalization of Spivey-type relation for degenerate Bell polynomials
by: Kim, Taekyun, et al.
Published: (2025)

Degenerate Algorithms for degenerate Bernoulli and Euler numbers
by: Kim, Taekyun, et al.
Published: (2026)

Probabilistic multi-Stirling numbers of the second kind and probabilistic multi-Lah numbers
by: Kim, Taekyun, et al.
Published: (2024)

Degenerate Eulerian polynomials and numbers
by: Kim, Taekyun, et al.
Published: (2024)

A note on new type degenerate Srirling numbers of the first kind
by: Kim, Taekyun, et al.
Published: (2025)

Probabilistic bivariate Bell polynomials
by: Kim, Taekyun, et al.
Published: (2024)

Combinatorial identities related to degenerate Stirling numbers of the second kind
by: Kim, Taekyun, et al.
Published: (2025)

Logarithms and Stirling numbers associated with delta series
by: Kim, Dae san, et al.
Published: (2026)

Degenerate Euler- Seidel Method for degenerate Bernoulli, Euler, and Genocchi polynomials
by: Kim, Taekyun, et al.
Published: (2025)

A probabilistic proof of a recurrence relation for sums of values of degenerate falling factorials
by: Kim, Taekyun, et al.
Published: (2024)

Probabilistic Stirling numbers associated with sequences
by: Kim, Dae San, et al.
Published: (2025)

Probabilistic degenerate Fubini polynomials associated with random variables
by: Xu, Rongrong, et al.
Published: (2024)

Probabilistic derangement numbers and polynomials
by: Kim, Taekyun, et al.
Published: (2024)

Probabilistic degenerate derangement polynomials
by: Kim, Taekyun, et al.
Published: (2024)

Several expressions for degenerate harmonic numbers and some related numbers
by: Kim, Taekyun, et al.
Published: (2025)

Degenerate Euler-Seidel Matrix Method and Their Applications
by: Kim, Taekyun, et al.
Published: (2025)

Probabilistic Lah numbers and Lah-Bell polynomials
by: Ma, Yuankui, et al.
Published: (2024)

Spivey's type recurrence relation for degenerate Bell polynomials
by: Kim, Taekyun, et al.
Published: (2025)

Spivey-type recurrence relation for fully degenerate Bell polynomials
by: Kim, Taekyun, et al.
Published: (2025)

Hurwitz--Lerch Type Families of Poly-Bernoulli and Poly-Cauchy Numbers and Polynomials with Parameters $(α,a)$
by: Lacpao, Noel B., et al.
Published: (2025)

$q$-analogues of sums of consecutive powers of natural numbers and extended Carlitz $q$-Bernoulli numbers and polynomials
by: Farhi, Bakir
Published: (2025)

Recurrence relations for degenerate Bell and Dowling polynomials via Boson operators
by: Kim, Taekyun, et al.
Published: (2025)

Probabilistic degenerate r-Stirling numbers of the second and probabilistic degenerate r-Bell polynomials
by: Kim, Taekyunj, et al.
Published: (2024)

Probabilistic proof of a summation formula
by: Kim, Taekyun, et al.
Published: (2024)

Generalization of Spivey's recurrence relation
by: Kim, Taekyun, et al.
Published: (2024)

Spivey's type recurrence relation for Lah-Bell polynomials
by: Kim, Taekyun, et al.
Published: (2025)

The asymptotics for the number of real roots of the Bernoulli polynomials
by: Efimov, A.
Published: (2006)

A short proof of Mathar's 2021 recurrence conjecture for the Lehmer-Comtet diagonal A045406
by: Niu, Tong
Published: (2026)

A short proof of Mathar's 2020 recurrence conjecture for the generalized-Stirling sequence A001711
by: Niu, Tong
Published: (2026)

A Generalized Recurrence for fully degenerate Bell polynomials
by: Kim, Taekyun, et al.
Published: (2025)

Operational Umbral Calculus
by: Beauduin, Kei
Published: (2024)

On Carmichael and polygonal numbers, Bernoulli polynomials, and sums of base-$p$ digits
by: Kellner, Bernd C., et al.
Published: (2019)

On the finiteness of Bernoulli polynomials whose derivative has only integral coefficients
by: Kellner, Bernd C.
Published: (2023)