EulerE

Notations

Traditional name

Traditional notation

Mathematica StandardForm notation

Primary definition

Specific values

Specialized values

Values at fixed points

General characteristics

Domain and analyticity

(Subscript[E, n]) is a nonanalytical function which is defined only for nonnegative integer n.

Symmetries and periodicities

Symmetry

No symmetry

Periodicity

No periodicity

Series representations

Generalized power series

Victor Adamchik

Asymptotic series expansions

Residue representations

Integral representations

On the real axis

Of the direct function

Contour integral representations

Limit representations

Generating functions

Identities

Identities involving determinants

Complex characteristics

Real part

Imaginary part

Absolute value

Argument

Conjugate value

Signum value

Summation

Finite summation

Infinite summation

Representations through more general functions

Through other functions

Involving Stirling numbers

Involving zeta functions

Representations through equivalent functions

With related functions

Inequalities

Zeros

History

– L. Euler (1755) use these numbers in series expansion for sec(z) near z==0
– H.  F. Scherk (1825) suggested the name and calculated the first 30 numbers
– G. Chrystal (1889) introduced modern notations
– L. Saalschütz (1893) found the relation between Euler and Bernoulli numbers

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