广义高阶Euler数的同余

Congruences for generalizations of higher-order Euler numbers

对于任意的正整数a,利用展开式1a(exp(t)+exp(-t))/2+1-()a k=∑∞n=0E(k)n,at nn!定义了一类广义k阶Euler数Ekn,a,并利用对比系数法,幂级数展开等初等方法得到一些相关的递推公式,同余式以及反转公式.

For a given positive integer a ,the generalizations of higher‐order Euler numbers Ekn ,a were defined by using 1a(exp(t)+ exp(- t))/2 + 1 - a k = ∑∞n= 0 E(k)n,a tnn!.By using the elemen‐tary methods ,several explicit formulas ,some congruences and an inversion formula for generali‐zations of higher‐order Euler numbers were obtained .