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EulerE

EulerE[n]
gives the Euler number .
EulerE
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.
First 10 EulerE numbers:
Euler polynomials:
First 10 EulerE numbers:
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Euler polynomials:
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EulerE threads element-wise over lists:
Plot Euler polynomials:
Simple exact values are generated automatically:
TraditionalForm formatting:
Implement the Boole summation formula:
First a sequence of approximations to ∑_(k=0)^n(-1)^kk^3:
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^(th) Euler number:
The sequence of Euler numbers mod a fixed number is periodic:
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