Note that B(n) is the n Bell number while S(n, k) is the Stirling number of the second kind. We have translated Spivey’s notation into Riordan’s familiar notation which we find more preferable in our work [5, 6]. The purpose of this note is to offer a short generating function proof of Equation (1). We discuss this proof in Section 2. We also use Spivey’s formula, in conjunction with the Stirli...

We establish an extension of Spivey’s Bell number formula and its associated Bell polynomial extension by using Hsu-Shiue’s generalized Stirling numbers. By means of the extension of Spivey’s Bell number formula we also extend Gould-Quaintance’s new Bell number formulas.

Bell peppers grown in greenhouses in the Mediterranean region are frequently subjected to high temperatures in summer and low temperatures in winter. The present experiment was designed to quantify the effect of season on pepper fruit growth, maturation and ripening. Three bell pepper (Capsicum annuum L.) cultivars (Yolo Wonder, California Wonder and E84066) were cultivated in an unheated ...