275 research outputs found
On Multi Poly-Bernoulli Polynomials
In this paper, we define multi poly-Bernoulli polynomials using multiple
polylogarithm and derive some properties parallel to those of poly-Bernoulli
polynomials. Furthermore, an explicit formula for certain Hurwitz-Lerch type
multi poly-Bernoulli polynomials is established using the -Whitney numbers
of the second kind.Comment: 15 pages. arXiv admin note: substantial text overlap with
arXiv:1512.0529
On Generalized Multi Poly-Euler and Multi Poly-Bernoulli Polynomials
In this paper, we establish more identities of generalized multi poly-Euler
polynomials with three parameters and obtain a kind of symmetrized
generalization of the polynomials. Moreover, generalized multi poly-Bernoulli
polynomials are defined using multiple polylogarithm and derive some properties
parallel to those of poly-Bernoulli polynomials. These are generalized further
using the concept of Hurwitz-Lerch multiple zeta values.Comment: 23 page
More Properties on Multi Poly-Euler Polynomials
In this paper, we establish more properties of generalized poly-Euler
polynomials with three parameters and we investigate a kind of symmetrized
generalization of poly- Euler polynomials. Moreover, we introduce a more
general form of multi poly-Euler polynomials and obtain some identities
parallel to those of the generalized poly-Euler polynomials.Comment: 17 page
Three-Parameter Logarithm and Entropy
A three-parameter logarithmic function is derived using the notion of
q-analogue and ansatz technique. The derived three-parameter logarithm is shown
to be a generalization of the two-parameter logarithmic function of Schwammle
and Tsallis as the latter is the limiting function of the former as the added
parameter goes to 1. The inverse of the three-parameter logarithm and other
important properties are also proved. A three-parameter entropic function is
then defined and is shown to be analytic and hence Lesche-stable, concave and
convex in some ranges of the parameters
Logarithmic Generalization of the Lambert W function and its Applications to Adiabatic Thermostatics of the Three-Parameter Entropy
A generalization of the Lambert W function called the logarithmic Lambert
function is found to be a solution to the thermostatics of the three-parameter
entropy of classical ideal gas in adiabatic ensembles. The derivative,
integral, Taylor series, approximation formula and branches of the function are
obtained. The thermostatics are computed and the heat functions are expressed
in terms of the logarithmic Lambert function.Comment: arXiv admin note: text overlap with arXiv:1210.5499 by other author
Translated Logarithmic Lambert Function and its Applications to Three-Parameter Entropy
The translated logarithmic Lambert function is defined and basic analytic
properties of the function are obtained including the derivative, integral,
Taylor series expansion, real branches and asymptotic approximation of the
function. Moreover, the probability distribution of the three-parameter entropy
is derived which is expressed in terms of the translated logarithmic Lambert
function.Comment: arXiv admin note: substantial text overlap with arXiv:2011.0428
Some Formulae of Genocchi Polynomials of Higher Order
In this paper, some formulae for Genoochi polynomials of higher order are
derived using the fact that sets of Bernoulli and Euler polynomials of higher
order form basis for the polynomial space
A Combinatorial Analysis Of Higher Order Generalised Geometric Polynomials: A Generalisation Of Barred Preferential Arrangements
A barred preferential arrangement is a preferential arrangement, onto which
in-between the blocks of the preferential arrangement a number of identical
bars are inserted. We offer a generalisation of barred preferential
arrangements by making use of the generalised Stirling numbers proposed by Hsu
and Shiue (1998). We discuss how these generalised barred preferential
arrangements offer a unified combinatorial interpretation of geometric
polynomials. We also discuss asymptotic properties of these numbers
A Note On Multi Poly-Euler Numbers And Bernoulli Polynomials
In this paper we introduce the generalization of Multi Poly-Euler polynomials
and we investigate some relationship involving Multi Poly-Euler polynomials.
Obtaining a closed formula for generalization of Multi Poly-Euler numbers
therefore seems to be a natural and important problem.Comment: 13 page
Generalized -Stirling numbers and normal ordering
The normal ordering coefficients of strings consisting of which satisfy
() are considered. These coefficients are studied
in two contexts: first, as a multiple of a sequence satisfying a generalized
recurrence, and second, as -analogues of rook numbers under the row creation
rule introduced by Goldman and Haglund. A number of properties are derived,
including recurrences, expressions involving other -analogues and explicit
formulas. We also give a Dobinsky-type formula for the associated Bell numbers
and the corresponding extension of Spivey's Bell number formula. The
coefficients, viewed as rook numbers, are extended to the case
via a modified rook model.Comment: New section on q-Bell numbers added, extended to case $s\in\mathbb R
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