We present computer-generated proofs of some summation identities for (q-)Stirling and (q-)Eulerian numbers that were obtained by combining a recent summation algorithm for Stirling number identities with a recurrence solver for difference fields.

The reported discrepancy between theory and experiment for external combustion Stirling engines is explained by the addition of thermal resistance of the combustion gasses to the standard Carnot model. In these cases, the Stirling engine ideal efficiency is not as is normally reported equal to the Carnot cycle efficiency but is significantly lower. A new equation for ideal Stirling engine effic...

We develop techniques that can be applied to find solutions to the recurrence ∣∣n k ∣∣ = ( n+ k + )∣∣n−1 k ∣∣+ ( ′n+ ′k + ′)∣∣n−1 k−1∣∣+ [n = k = 0]. Many interesting combinatorial numbers, such as binomial coefficients, both kinds of Stirling and associated Stirling numbers, Lah numbers, Eulerian numbers, and second-order Eulerian numbers, satisfy special cases of this recurrence. Our techniqu...

Stirling et al. (2003) reported the discovery of a 2.3 year periodic variation in the structural position angle of the parsec-scale radio core in the blazar BL Lac. We searched for independent confirmation of this periodic behavior using 43 GHz images of the radio core during ten epochs overlapping those of Stirling et al. Our maps are consistent with several periodicities, including one near t...

The Dish Stirling systems have demonstrated the highest efficiency of any solar power generation system by converting nearly 31.25% [1] of direct normal incident solar radiation into electricity after accounting for parasitic power losses. Therefore, the Dish Stirling technology is anticipated to surpass parabolic troughs by producing power at more economical rates and higher efficiencies. Beca...

It is shown that the Stirling numbers of the first kind can be expressed in the form [n k ] = ∑n−1 j1<j2<···<jk−1 (n−1)! αQ[j1,j2,...,jk−1] , where Q is a product of k − 1 linear factors in the indices j1, j2, . . . , jk−1 and α is a normalization coefficient determined by the condition [ k k ] = 1. Several types of Q’s are shown to yield Stirling numbers (“be Stirling”), and some more are conj...

The Jacobi-Stirling numbers of the first and second kind were introduced in 2007 by Everitt et al. In this article we find new explicit formulas for Jacobi Stirling numbers. Furthermore, derive study class so-called generalized Some special cases such as Legendre-Stirling are given. interesting combinatorial identities obtained.

A new family of generalized Stirling and Bell numbers is introduced by considering powers (V U)n of the noncommuting variables U, V satisfying UV = V U +hV s. The case s = 0 (and h = 1) corresponds to the conventional Stirling numbers of second kind and Bell numbers. For these generalized Stirling numbers, the recursion relation is given and explicit expressions are derived. Furthermore, they a...

Abstract. Inversion formulas have been found, converting between Stirling, tanh and Lah numbers. Tanh and Lah polynomials, analogous to the Stirling polynomials, have been defined and their basic properties established. New identities for Stirling and tangent numbers and polynomials have been derived from the general inverse relations. In the second part of the paper, it has been shown that if ...

The Stirling number of the second kind {k} counts the number of ways to partition a set of n labeled balls into k non-empty unlabeled cells. We extend this problem and give a new statement of the r-Stirling numbers of the second kind and r-Bell numbers. We also introduce the r-mixed Stirling number of the second kind and r-mixed Bell numbers. As an application of our results we obtain a formula...