161,628 research outputs found
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
Computer Algebra meets Finite Elements: an Efficient Implementation for Maxwell's Equations
We consider the numerical discretization of the time-domain Maxwell's
equations with an energy-conserving discontinuous Galerkin finite element
formulation. This particular formulation allows for higher order approximations
of the electric and magnetic field. Special emphasis is placed on an efficient
implementation which is achieved by taking advantage of recurrence properties
and the tensor-product structure of the chosen shape functions. These
recurrences have been derived symbolically with computer algebra methods
reminiscent of the holonomic systems approach.Comment: 16 pages, 1 figure, 1 table; Springer Wien, ISBN 978-3-7091-0793-
Parafermionic polynomials, Selberg integrals and three-point correlation function in parafermionic Liouville field theory
In this paper we consider parafermionic Liouville field theory. We study
integral representations of three-point correlation functions and develop a
method allowing us to compute them exactly. In particular, we evaluate the
generalization of Selberg integral obtained by insertion of parafermionic
polynomial. Our result is justified by different approach based on dual
representation of parafermionic Liouville field theory described by
three-exponential model
Systems of orthogonal polynomials defined by hypergeometric type equations with application to quantum mechanics
A hypergeometric type equation satisfying certain conditions defines either a
finite or an infinite system of orthogonal polynomials. We present in a unified
and explicit way all these systems of orthogonal polynomials, the associated
special functions and the corresponding raising/lowering operators. The
considered equations are directly related to some Schrodinger type equations
(Poschl-Teller, Scarf, Morse, etc), and the defined special functions are
related to the corresponding bound-state eigenfunctions.Comment: Additional results available at
http://fpcm5.fizica.unibuc.ro/~ncotfa
Spin networks and SL(2,C)-Character varieties
Denote the free group on 2 letters by F_2 and the SL(2,C)-representation
variety of F_2 by R=Hom(F_2,SL(2,C)). The group SL(2,C) acts on R by
conjugation. We construct an isomorphism between the coordinate ring C[SL(2,C)]
and the ring of matrix coefficients, providing an additive basis of
C[R]^SL(2,C) in terms of spin networks. Using a graphical calculus, we
determine the symmetries and multiplicative structure of this basis. This gives
a canonical description of the regular functions on the SL(2,C)-character
variety of F_2 and a new proof of a classical result of Fricke, Klein, and
Vogt.Comment: Updated historical treatment of the subject. Figures drawn with
PGF/TikZ; Handbook of Teichmuller Theory II, A. Papadopoulos (ed), EMS
Publishing House, Zurich, 200
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