gives the Euler number .
gives the Euler polynomial .
- Mathematical function, suitable for both symbolic and numerical manipulation.
- The Euler polynomials satisfy the generating function relation .
- The Euler numbers are given by .
- EulerE automatically threads over lists.
Examplesopen allclose all
Basic Examples (2)
First 10 EulerE numbers:
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:
Properties & Relations (5)
Possible Issues (1)
Algorithmically produced results are often expressed using Zeta instead of EulerE:
Neat Examples (3)
Umbral calculus with Euler numbers:
Histogram of digits of 10000 Euler number:
The sequence of Euler numbers mod a fixed number is periodic: