168 research outputs found
The Reversed q-Exponential Functional Relation
After obtaining some useful identities, we prove an additional functional
relation for exponentials with reversed order of multiplication, as well as
the well known direct one in a completely rigorous manner.Comment: 6 pages, LaTeX, no figure
On Fourier integral transforms for -Fibonacci and -Lucas polynomials
We study in detail two families of -Fibonacci polynomials and -Lucas
polynomials, which are defined by non-conventional three-term recurrences. They
were recently introduced by Cigler and have been then employed by Cigler and
Zeng to construct novel -extensions of classical Hermite polynomials. We
show that both of these -polynomial families exhibit simple transformation
properties with respect to the classical Fourier integral transform
h analogue of Newton's binomial formula
In this letter, the --analogue of Newton's binomial formula is obtained in
the --deformed quantum plane which does not have any --analogue. For
, this is just the usual one as it should be. Furthermore, the binomial
coefficients reduce to for . \\ Some properties of the
--binomial coefficients are also given. \\ Finally, I hope that such results
will contribute to an introduction of the --analogue of the well--known
functions, --special functions and --deformed analysis.Comment: 6 pages, latex Jounal-ref: J. Phys. A: Math. Gen. 31 (1998) L75
Exactly solvable D_N-type quantum spin models with long-range interaction
We derive the spectra of the D_N-type Calogero (rational) su(m) spin model,
including the degeneracy factors of all energy levels. By taking the strong
coupling limit of this model, in which its spin and dynamical degrees of
freedom decouple, we compute the exact partition function of the su(m)
Polychronakos-Frahm spin chain of D_N type. With the help of this partition
function we study several statistical properties of the chain's spectrum, such
as the density of energy levels and the distribution of spacings between
consecutive levels.Comment: 12 pages, 2 figure
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
High mammographic density is associated with an increase in stromal collagen and immune cells within the mammary epithelium
Schnell konvergierende Ziffernverteilungen bei speziellen Zahlentheoretischen Transformationen
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