Some formulae of products of the Apostol-Bernoulli and Apostol-Euler polynomials

DOI10.1155/2012/927953zbMath1263.11032OpenAlexW2166620770WikidataQ58700861 ScholiaQ58700861MaRDI QIDQ714298

Yuan He, Chunping Wang

Publication date: 19 October 2012

Published in: Discrete Dynamics in Nature and Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2012/927953

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68)

Related Items (12)

Some symmetry identities for the Apostol-type polynomials related to multiple alternating sums ⋮ Some new identities for the Apostol-Bernoulli polynomials and the Apostol-Genocchi polynomials ⋮ New formulae of products of the Frobenius-Euler polynomials ⋮ Summation formulae of products of the Apostol-Bernoulli and Apostol-Euler polynomials ⋮ New recurrence formulae for the Apostol-Bernoulli and Apostol-Euler polynomials ⋮ Recurrence formulae for Apostol-Bernoulli and Apostol-Euler polynomials ⋮ Extended \(p\)-adic \(q\)-invariant integrals on \(\mathbb{Z}_p\) associated with applications of umbral calculus ⋮ A new formula of products of the Apostol-Bernoulli and Apostol-Euler polynomials ⋮ Some new formulae for Genocchi numbers and polynomials involving Bernoulli and Euler polynomials ⋮ Sums of products of Apostol-Bernoulli and Apostol-Euler polynomials ⋮ On the extended kim's \(p\)-adic \(q\)-deformed fermionic integrals in the \(p\)-adic integer ring ⋮ Some new results on products of Apostol-Bernoulli and Apostol-Euler polynomials

Cites Work

• Some generalizations of the Apostol-Bernoulli and Apostol-Euler polynomials
• Some new identities on the Bernoulli and Euler numbers
• New identities involving Bernoulli and Euler polynomials
• An explicit formula for the generalized Bernoulli polynomials
• Remarks on some relationships between the Bernoulli and Euler polynomials.
• On the Lerch zeta function
• Fourier expansions and integral representations for the Apostol-Bernoulli and Apostol-Euler polynomials
• Some sum relations involving Bernoulli and Euler polynomials
• Note on the Integral of the Product of Several Bernoulli Polynomials
• The multiplication formulas for the Apostol–Bernoulli and Apostol–Euler polynomials of higher order
• Some formulas for the Bernoulli and Euler polynomials at rational arguments

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