10,041 research outputs found
Some New Identities of Genocchi Numbers and Polynomials involving Bernoulli and Euler polynomials
In this paper, we will deal with some new formulae for two product Genocchi
polynomials together with both Euler polynomials and Bernoulli polynomials. We
get some applications for Genocchi polynomials. Our applications possess a
number of interesting properties to study in Theory of Analytic numbers which
we express in the present paper.Comment: 10 pages, submitte
Euler Polynomials and Identities for Non-Commutative Operators
Three kinds of identities involving non-commutating operators and Euler and
Bernoulli polynomials are studied. The first identity, as given by Bender and
Bettencourt, expresses the nested commutator of the Hamiltonian and momentum
operators as the commutator of the momentum and the shifted Euler polynomial of
the Hamiltonian. The second one, due to J.-C. Pain, links the commutators and
anti-commutators of the monomials of the position and momentum operators. The
third appears in a work by Figuieira de Morisson and Fring in the context of
non-Hermitian Hamiltonian systems. In each case, we provide several proofs and
extensions of these identities that highlight the role of Euler and Bernoulli
polynomials.Comment: 20 page
Central factorials under the Kontorovich-Lebedev transform of polynomials
We show that slight modifications of the Kontorovich-Lebedev transform lead
to an automorphism of the vector space of polynomials. This circumstance along
with the Mellin transformation property of the modified Bessel functions
perform the passage of monomials to central factorial polynomials. A special
attention is driven to the polynomial sequences whose KL-transform is the
canonical sequence, which will be fully characterized. Finally, new identities
between the central factorials and the Euler polynomials are found.Comment: also available at http://cmup.fc.up.pt/cmup/ since the 2nd August
201
Pohozhaev and Morawetz Identities in Elastostatics and Elastodynamics
We construct identities of Pohozhaev type, in the context of elastostatics
and elastodynamics, by using the Noetherian approach. As an application, a
non-existence result for forced semi-linear isotropic and anisotropic elastic
systems is established
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