An Explicit Formula for the Euler Polynomials of Higher Order

作者：Luo Qiu Ming^*

来源：Applied Mathematics and Information Sciences, 2009, 3(1): 53-58.

• Euler numbers of higher order
• Euler polynomials of higher order
• Gaussian hypergeometric function
• Stirling numbers of the second kind
• difference operator
• coding theory and cryptography

We obtain an explicit formula for the Euler polynomials of higher order in terms of the Gaussian hypergeometric function. The corresponding new formulas of the Euler polynimials and numbers are also deduced. Finally, we also remark some possible applications of these results in the number theory and information science fields.

• 出版日期2009-1
• 单位华东师范大学; 焦作大学