this paper presents a proof of stirling's formula using haar wavelets and some properties of hilbert space, such as parseval's identity. the present paper shows a connection between haar wavelets and certain sequences.

We investigate some algorithms that produce Bernoulli, Euler and Genocchi polynomials. We also give closed formulas for Bernoulli, Euler and Genocchi polynomials in terms of weighted Stirling numbers of the second kind, which are extensions of known formulas for Bernoulli, Euler and Genocchi numbers involving Stirling numbers of the second kind.

SEXY STREAMERS? THE ROLE OF NATURAL AND SEXUAL SELECTION IN THE EVOLUTION OF HIRUNDINE TAIL STREAMERS Park, K.J., Buchanan, K.L. and Evans, M.R. Department of Biological Sciences, University of Stirling, Stirling FK9 4LA, U.K. 1 [email protected] 2 [email protected] [email protected]

In this paper, we define the generating functions for the generalized q-Stirling numbers of the second kind. By applying Mellin transform to these functions, we construct interpolation functions of these numbers at negative integers. We also derive some identities and relations related to q-Bernoulli numbers and polynomials and q-Stirling numbers of the second kind.

Grace, A. P. (2009). Resilient sexual-minority youth as fugitive lifelong learners: Engaging in a strategic, assetcreating, community-based learning process to counter exclusion and trauma in formal schooling. In J. Field (Ed.), Proceedings of the Lifelong Learning Revisited: What Next? Conference of the Scottish Centre for Research in Lifelong Learning, University of Stirling, Stirling, UK (4,...

The Bell number B(G) of a simple graph G is the number of partitions of its vertex set whose blocks are independent sets of G. The number of these partitions with k blocks is the (graphical) Stirling number S(G, k) of G. We explore integer sequences of Bell numbers for various one-parameter families of graphs, generalizations of the relation B(Pn) = B(En−1) for path and edgeless graphs, one-par...

P.L. Erdős and L.A. Székely [Adv. Appl. Math. 10(1989), 488– 496] gave a bijection between rooted semilabeled trees and set partitions. L.H. Harper’s results [Ann. Math. Stat. 38(1967), 410–414] on the asymptotic normality of the Stirling numbers of the second kind translates into asymptotic normality of rooted semilabeled trees with given number of vertices, when the number of internal vertice...

We define a new class of generating function transformations related to polylogarithm functions, Dirichlet series, and Euler sums. These transformations are given by an infinite sum over the jth derivatives of a sequence generating function and sets of generalized coefficients satisfying a non-triangular recurrence relation in two variables. The generalized transformation coefficients share a n...

Stirling engine technologies have been applied to cogeneration systems mainly for residential applications. The performance of Stirling engines has been evaluated considering different operational conditions, which include the electrical and thermal production. Thermodynamic analysis of the Stirling engine’s performance has been conducted, using specially designed computing codes along with the...

Claire Fortunel*, C. E. Timothy Paine, Paul V. A. Fine, Nathan J. B. Kraft and Christopher Baraloto INRA, UMR Ecologie des Forêts de Guyane, BP 709, 97387, Kourou Cedex, France; Biological and Environmental Sciences, University of Stirling, Stirling FK9 4LA, UK; Department of Integrative Biology, University of California, Berkeley, CA 94720, USA; Department of Biology University of Maryland, Co...