First 10 EulerE numbers:

Euler polynomials:

EulerE threads elementwise over lists:

Plot Euler polynomials:

Simple exact values are generated automatically:

TraditionalForm formatting:

Implement the Boole summation formula:

First a sequence of approximations to :

The sequence converges to the exact answer:

Plot roots of Euler polynomials in the complex plane:

Find Euler numbers from their generating function:

Find Euler polynomials from their generating function:

EulerE can be represented as a DifferenceRoot:

FindSequenceFunction can recognize the EulerE sequence:

The exponential generating function for EulerE:

Algorithmically produced results are often expressed using Zeta instead of EulerE:

Umbral calculus with Euler numbers:

Histogram of digits of 10000 Euler number:

The sequence of Euler numbers modulo a fixed number is periodic:

Define a Hankel matrix whose entries are the Euler numbers:

Its determinant can be expressed in terms of the Barnes G-function: