Hermite base Bernoulli type polynomials on the umbral algebra

DOI10.1134/S106192081501001XzbMath1318.33015OpenAlexW3098749442MaRDI QIDQ2354094

Yilmaz Simsek, Rahime Dere

Publication date: 10 July 2015

Published in: Russian Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s106192081501001x

zbMATH Keywords

Stirling numbersHermite polynomialsBernoulli polynomialsMilne-Thomson polynomials

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Bell and Stirling numbers (11B73) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45)

Related Items (16)

Normalized polynomials and their multiplication formulas ⋮ Identities associated with Milne-Thomson type polynomials and special numbers ⋮ A new generalization of Apostol-type Laguerre-Genocchi polynomials ⋮ Fully degenerate poly-Bernoulli numbers and polynomials ⋮ A new class of generalized polynomials associated with Hermite and Euler polynomials ⋮ Representations of degenerate Hermite polynomials ⋮ On a class of generalized Humbert-Hermite polynomials via generalized Fibonacci polynomials ⋮ Some identities of degenerate harmonic and degenerate hyperharmonic numbers arising from umbral calculus ⋮ Formulae bringing to light from certain classes of numbers and polynomials ⋮ Explicit, determinantal, recursive formulas, and generating functions of generalized Humbert–Hermite polynomials via generalized Fibonacci polynomials ⋮ A new class of generalized polynomials ⋮ A new class of generalized polynomials involving Laguerre and Euler polynomials ⋮ A new class of generalized polynomials associated with Laguerre and Bernoulli polynomials ⋮ Formulas for Poisson-Charlier, Hermite, Milne-Thomson and other type polynomials by their generating functions and \(p\)-adic integral approach ⋮ Representations of degenerate poly-Bernoulli polynomials ⋮ Some recurrence formulas for the q-Bernoulli and q-Euler polynomials

Cites Work

• Unnamed Item
• A note on sums of products of Bernoulli numbers
• Genocchi polynomials associated with the umbral algebra
• Representations of monomiality principle with Sheffer-type polynomials and boson normal ordering
• Multidimensional extensions of the Bernoulli and Appell polynomials
• Sheffer polynomials, monomiality principle, algebraic methods and the theory of classical polynomials

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