Author(s)

Do Tan Si

Ho Chi Minh-City Physical Association, Ho Chi Minh-City, Vietnam.

Utilization of the shift operator to represent Euler polynomials as polynomials of Appell type leads directly to its algebraic properties, its relations with powers sums; may be all its relations with Bernoulli polynomials, Bernoulli numbers; its recurrence formulae and a very simple formula for calculating simultaneously Euler numbers and Euler polynomials. The expansions of Euler polynomials into Fourier series are also obtained; the formulae for obtaining all π^m as series on k^-m and for expanding functions into series of Euler polynomials.

Obtaining Appell Type Euler Numbers and Polynomials, Relations Euler-Bernoulli Polynomials, Sums over k^m, Series on k^-m, Euler Series of Functions

Si, D. (2023) Obtaining Simply Explicit Form and New Properties of Euler Polynomials by Differential Calculus. Applied Mathematics, 14, 460-480. doi: 10.4236/am.2023.147029.