Stirling Numbers
Explicit expressions and integral representations for the Stirling numbers A probabilistic approach
... The Stirling numbers play an important role in many branches of mathematics and physics as ingredients in the computation of diverse ...such numbers (see the references in ...
11
On (q, r, w)-Stirling Numbers of the Second Kind
... r-Stirling numbers of the second kind based on the q-numbers via an exponential gen- erating ...q-Bernoulli numbers and polynomials, and newly de…ned (q; r; w)- Stirling numbers ...
8
Gram matrices and Stirling numbers of a class of diagram algebras, I
... A b s t r ac t . In this paper, we introduce Gram matrices for the signed partition algebras, the algebra of Z 2 -relations and the par- tition algebras. The nondegeneracy and symmetic nature of these Gram matrices are ...
25
Gram matrices and Stirling numbers of a class of diagram algebras, II
... A b s t r ac t . In the paper [6], we introduced Gram matrices for the signed partition algebras, the algebra of Z 2 -relations and the partition algebras. (s 1 , s 2 , r 1 , r 2 , p 1 , p 2 )-Stirling ...
42
SOME IDENTITIES RELATING TO EULERIAN POLYNOMIALS AND INVOLVING STIRLING NUMBERS
... the Stirling numbers of the sec- ond kind, and present two identities for Eulerian polynomials and higher order Eulerian polynomials, pose two open problems about summability of two fi- nite sums involving ...
10
Generalized Legendre Stirling Numbers
... Legendre-Stirling numbers were discovered by Everitt, Littlejohn and Wellman in 2002 in a study of the spectral theory of powers of the classical second-order Legendre differential ...these numbers ...
7
Stirling Numbers and Generalized Zagreb Indices
... proliferation of other graph polynomials, it is surprising that this polynomial attracted no attention of researchers so far. In the following we show that the degree sequence polynomial encodes far more information on G ...
5
On Polynomials Rn(x) Related to the Stirling Numbers and the Bell Polynomials Associated with the p Adic Integral on
... On Polynomials Rn x Related to the Stirling Numbers and the Bell Polynomials Associated with the p-Adic Integral on p Hui Young Lee*, Cheon Seoung Ryoo Department of Mathematics, Han[r] ...
10
A research on the new polynomials involved with the central factorial numbers, Stirling numbers and others polynomials
... 7. Kim, M-S, Lee, JH: On sums of products of the extended q-Euler numbers. J. Math. Anal. Appl. 397, 522-528 (2013) 8. Kim, M-S: On Euler numbers, polynomials and related p-adic integrals. J. Number Theory ...
10
Generating functions for generalized Stirling type numbers, Array type polynomials, Eulerian type polynomials and their applications
... Genocchi numbers and polynomials and also their generalizations, the λ-Stirling numbers of the second kind, the array polynomials and the Eulerian polynomials, related to nonnegative real parameters, ...
28
Some Convolution-Type Identities of a q-Analogue of Second Kind r-Whitney Numbers
... 𝛽)-Stirling numbers in terms of the occupancy distribution which, consequently, gave some probability distributions that are useful establishing their statistical ...𝛽)-Stirling numbers is ...
9
On a Class of Combinatorial Sums Involving Generalized Factorials
... the numbers S ( p , r ; θ , 1, j ), S ( p , r ; 0, 1, j ), and S ( p , r ; θ , 1, 0), which are known as Howard’s degenerate weighted Stirling numbers, Carlitz’s weighted Stirling ...
9
Generating function for q-Eulerian polynomials and their decomposition and applications
... as Stirling numbers, Array polynomials ...special numbers and polynomials, it is worth depict- ing these references as ...and numbers (q-Apostol-type ...
14
On a q-Analogue of the Non-central Whitney Numbers
... Stirling numbers was extensively studied by several mathematicians due to its applications in deferent field of discipline and its relatively interesting correlation properties with other branches of ...
12
Generalized Eulerian Numbers
... k = appear in quantum optics for coherent phase states in the calculation of some kind of expectation values. We discuss some properties of the numbers E µ ( ) k l , and derive the recurrence relations for them. ...
27
Simplification of Coefficients in Differential Equations Associated with Higher Order Frobenius–Euler Numbers
... binomial numbers and the Stirling numbers of the first and second kinds, the authors simplify meaningfully and significantly coefficients in two families of ordinary differential equations associated ...
7
Modified degenerate Carlitz's $q$-bernoulli polynomials and numbers with weight ($\alpha ,\beta $)
... and numbers with weight (α, β), and satisfies some identities and properties of ...and numbers with weight (α, β) and investigate their some identities and relations related to Stirling ...
10
Modified Degenerate Carlitz’s q-Bernoulli Polynomials and Numbers with Weight (α, β)
... and numbers with weight (α, β), and satisfies some identities and properties of ...and numbers with weight (α, β) and investigate their some identities and relations related to Stirling ...
11
SERIES REPRESENTATION OF POWER FUNCTION
... Identity, Stirling numbers of second kind, Faulhabers sum, finite difference, Faulhabers formula, central factorial numbers, binomial coefficients, Binomial distribution, binomial transform, ...
27
ON THE DEGENERATE h, q -CHANGHEE NUMBERS AND POLYNOMIALS
... In this paper, we defined two types of the degenerate (h, q)-Changhee polyno- mials and number, and found the relationship between the Stirling numbers of the first kind and second kind, q-Euler ...
14