The 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 ...
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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] ...
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On (q, r, w)-Stirling Numbers of the Second Kind
... r-Stirling numbers, which is most cases generalize similar properties of the regular Stirling ...the Stirling numbers, termed weighted Stirling ...of Stirling ...
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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 ...
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Special Numbers on Analytic Functions
... The Stirling numbers of the first and the second are used in pure and applied ...The Stirling number of the second kind, denoted by S n k ( ) , , is the number of ways to partition a set of n objects ...
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Identities, inequalities for Boole type polynomials: approach to generating functions and infinite series
... combinatorial numbers and polynomials, and for Peters type polynomials with the help of their generating ...special numbers and polynomials such as Stirling numbers, the Apostol–Euler ...
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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 ...
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Modified degenerate Carlitz's $q$-bernoulli polynomials and numbers with weight ($\alpha ,\beta $)
... bers with weight (α, β) and obtain some recurrence relations and other identities. Moreover, we derive some correlations with the modified Carlitz’s q-Bernoulli polynomials with weight (α, β), the modified degenerate ...
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Identities associated with Milne–Thomson type polynomials and special numbers
... Bernoulli numbers, the Euler numbers, the Stirling numbers, the central factorial numbers, and the Cauchy ...these numbers and polynomials, and also the combinatorial ...
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Generalized Legendre Stirling Numbers
... The Stirling numbers of the second kind have long played an important role in many areas of combinatorics and have a nice combinatorial interpretation in terms of set partitions (for example, see ...the ...
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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. ...
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... Abstract. In this article, authors introduce a new class of degenerate Hermite poly- Genocchi polynomials and give some identities of these polynomials related to the Stirling numbers of the second kind. ...
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Several closed expressions for the Euler numbers
... Bernoulli numbers, the Genocchi numbers, the tangent numbers, the Euler polynomials, the Stirling numbers of two kinds, and the Riemann zeta function, in number theory and ...
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Stirling Numbers and Generalized Zagreb Indices
... The Zagreb indices belong to the oldest and the best researched topological indices.Since their introduction in early seventies [7] they have also given rise to numerous generalizations. (For a survey, see [6].) In this ...
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Simplifying Coefficients in Differential Equations Associated with Higher Order Bernoulli Numbers of the Second Kind
... the Stirling numbers of the first and second kinds, the authors establish meaning- fully and significantly two identities which simplify coefficients in a family of ordinary differential equations ...
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Modified Degenerate Carlitz’s q-Bernoulli Polynomials and Numbers with Weight (α, β)
... polynomials and numbers with weight (α, β) and obtain some recurrence relations and other iden- tities. Moreover, we derive some correlations with the modified Carlitz’s q-Bernoulli polynomials with weight (α, β), ...
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Some Convolution-Type Identities of a q-Analogue of Second Kind r-Whitney Numbers
... Bell numbers 𝐵 𝑛 . That is, 𝐵 𝑛 = 𝐵 𝑛 (1). All other Bell-type numbers and polynomials are defined in this ...Bell-type numbers and polynomials possess several combinatorial properties and ...
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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 ...
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On a q-Analogue of the Non-central Whitney Numbers
... Whitney numbers of both kinds are define in terms of horizontal generating ...Dowling numbers and polynomials are defining and establish some of their ...
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Power Generation Using Rural Cooking Method
... of stirling engine generator and solar panel electricity ...to Stirling engine generator. Heating up of stirling engine The Stirling engine piston is coupled with fan-magnet setup creating ...
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