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 sh...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.展开更多
Using the generating functions, we prove some symmetry identities for the Euler polynomials and higher order Euler polynomials, which generalize the multiplication theorem for the Euler polynomials. Also we obtain som...Using the generating functions, we prove some symmetry identities for the Euler polynomials and higher order Euler polynomials, which generalize the multiplication theorem for the Euler polynomials. Also we obtain some relations between the Bernoulli polynomials, Euler polynomials, power sum, alternating sum and Genocchi numbers.展开更多
基金Supported by the Natural Science Foundation of Gansu Province (Grant No.1010RJZA049)
文摘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.
基金Supported by the Natural Science Foundation of Gansu Province (Grant No. 3ZS041-A25-007)
文摘Using the generating functions, we prove some symmetry identities for the Euler polynomials and higher order Euler polynomials, which generalize the multiplication theorem for the Euler polynomials. Also we obtain some relations between the Bernoulli polynomials, Euler polynomials, power sum, alternating sum and Genocchi numbers.
