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Mathematica > Mathematics and Algorithms > Calculus > Discrete Calculus > Recurrence and Sum Functions > EulerE >

BUILT-IN MATHEMATICA SYMBOL

EulerE

EulerE[n]
gives the Euler number

gives the Euler polynomial

First 10 EulerE numbers:

Euler polynomials:

First 10 EulerE numbers:

Out[1]=

Euler polynomials:

Out[1]=

EulerE threads element-wise over lists:

Plot Euler polynomials:

Simple exact values are generated automatically:

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:

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 mod a fixed number is periodic: