Congruences And Correlated Identities Of Generalized Euler Numbers

Euler number comes from combination of mathematics. It has a close re-lationship among Fibonacci numbers, Bernoulli numbers, and Central factorial numbers.Therefore, scholars both at home and aboard research on it. A lot of identity and congruence about Euler number are got by scholars, such as Zhang Wenpeng, Liu Guodong, Sun Zhihong. Based on previous studies,we have fur-ther research on the general form of the Euler numbers.The main results are presented as follows:First of all, summary definitions and basic properties about variety form of Euler numbers. On the basis of their results, we got many identities between different form of Euler numbers.Secondly, for given real numbers a, b, c, using this formula elementary methods to obtain several explicit formulas, some congruences and an inversion formula for generalizations of higher-order Euler numbers. polynomials use of contrast coefficient method and power series ex-pansion method, structure method, we got some identities of generalizations of higher-order Euler polynomials.