Some Positivities in Stirling Arrays with Higher Level

Generalized higher order Stirling numbers

on some bayesian statistical models in actuarial science with emphasis on claim count

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Some robust higher-level percepts for music.

We explored a range of higher-level percepts in music. Participants were asked to make two-alternative forced-choice judgments of extracts of instrumental music on various dipole categories, such as happy/sad or male/female. The consistency with which each stimulus was judged on a response category across listeners provides an indication of the extent to which the musical percept can be mapped ...

Some Remarks on the Stirling Numbers

Sdn, n-k)= L B1 (k, j) j=1 and k C+:;I). S(n, n-k) = L B(k, j) j~1 Moreover (1. 6) B1 (k, j)=B(k, k-j+ 1) (1 ~j~k). 1. The Stirling numbers SI (n, k), S (n, k) of the first and second kind Tespectively, can be defined by (1.1) n x(x+l).. .(x+n-l)-L SI(n, k)Xk k=O .and (1.2) n xn= L S(n, k)x(x~ 1).. .(x-k+ 1). k=O Also it is well known that SI (n,n-k) and S(n, n-k) are polynomials in n ~f degree...

Some Properties of Associated Stirling Numbers

Abstract In this paper, we discuss the properties of associated Stirling numbers. By means of the method of coefficients, we establish a series of identities involving associated Stirling numbers, Bernoulli numbers, harmonic numbers, and the Cauchy numbers of the first kind. In addition, we give the asymptotic expansion of certain sums involving 2-associated Stirling numbers of the second kind ...