Finance

Orthogonal polynomials

Physics

Algebra over a field

Bernoulli's principle

Bell polynomials

Economics

Stirling number

Order (exchange)

Bernoulli polynomials

Pure mathematics

Classical orthogonal polynomials

Stirling numbers of the second kind

Mathematics

Discrete orthogonal polynomials

Difference polynomials

Thermodynamics

Axioms

In this paper, we consider Bell-based Stirling polynomials of the second kind and derive some useful relations and properties including some summation formulas related to the Bell polynomials and Stirling numbers of the second kind. Then, we introduce Bell-based Bernoulli polynomials of order α and investigate multifarious correlations and formulas including some summation formulas and derivative properties. Also, we acquire diverse implicit summation formulas and symmetric identities for Bell-based Bernoulli polynomials of order α. Moreover, we attain several interesting formulas of Bell-based Bernoulli polynomials of order α arising from umbral calculus.

Bell-Based Bernoulli Polynomials with Applications