The Bessel Numbers and Bessel Matrices

In this paper, using exponential Riordan arrays, we investigate the Bessel numbers and Bessel matrices. By exploring links between the Bessel matrices, the Stirling matrices and the degenerate Stirling matrices, we show that the Bessel numbers are special case of the degenerate Stirling numbers, and derive explicit formulas for the Bessel numbers in terms of the Stirling numbers and binomial coefficients. Keywords Bessel number of the first kind; Bessel number of the second kind; exponential Riordan array; Stirling numbers; Bessel matrix.

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