%0 Journal Article
%T Obtaining Simply Explicit Form and New Properties of Euler Polynomials by Differential Calculus
%A Do Tan Si
%J Applied Mathematics
%P 460-480
%@ 2152-7393
%D 2023
%I Scientific Research Publishing
%R 10.4236/am.2023.147029
%X 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 <i>¦Ð<sup>m</sup></i> as series on <i>k<sup>-m</sup></i> and for expanding functions into series of Euler polynomials.
%K Obtaining Appell Type Euler Numbers and Polynomials
%K Relations Euler-Bernoulli Polynomials
%K Sums over &lt
%K i&gt
%K k&lt
%K sup&gt
%K m&lt
%K /sup&gt
%K &lt
%K /i&gt
%K Series on &lt
%K i&gt
%K k&lt
%K sup&gt
%K -m&lt
%K /sup&gt
%K &lt
%K /i&gt
%K Euler Series of Functions
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=126610