A note on harmonic numbers, umbral calculus and generating functions

DOI10.1016/j.aml.2007.07.021zbMath1152.05306OpenAlexW2070260022MaRDI QIDQ998570

Giuseppe Dattoli, Hari M. Srivastava

Publication date: 29 January 2009

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2007.07.021

zbMATH Keywords

generating functionsumbral calculusLaguerre polynomialsBessel functionharmonic numbersKampé de Fériet polynomialsmonomiality principleoperational identitiesGaussian identity

Mathematics Subject Classification ID

Umbral calculus (05A40) Hypergeometric functions (33C99)

Related Items (21)

A new generalization of hyperharmonic numbers ⋮ Exponential generating function of hyperharmonic numbers indexed by arithmetic progressions ⋮ A novel proof of two partial fraction decompositions ⋮ Finite Hurwitz-Lerch functions ⋮ Some extensions for the several combinatorial identities ⋮ Finite summation formulas involving binomial coefficients, harmonic numbers and generalized harmonic numbers ⋮ Negative derivatives and special functions ⋮ Some summation formulas involving harmonic numbers and generalized harmonic numbers ⋮ Certain summation formulas involving harmonic numbers and generalized harmonic numbers ⋮ Summation formulas involving binomial coefficients, harmonic numbers, and generalized harmonic numbers ⋮ Sums of quadratic half integer harmonic numbers of alternating type ⋮ The Dattoli-Srivastava conjectures concerning generating functions involving the harmonic numbers ⋮ A new approach to Legendre-truncated-exponential-based Sheffer sequences via Riordan arrays\(^\star \) ⋮ Umbral methods and harmonic numbers ⋮ Efficient approximations of finite and infinite real alternating p -series ⋮ On the distributions of infinite server queues with batch arrivals ⋮ Quadratic alternating harmonic number sums ⋮ Harmonic sums and integral representations ⋮ A Riordan array approach to Apostol type-Sheffer sequences ⋮ On a series of Ramanujan, dilogarithm values, and solitons ⋮ Identities for the shifted harmonic numbers and binomial coeffecients

Cites Work

• Generalized polynomials, operational identities and their applications
• Some expansions of the exponential integral in series of the incomplete Gamma function
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