Skip to content

E

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

E
    is the exponential constant e (base of natural logarithms), with
    numerical value ~= 2.71828.
E is a mathematical constant: it has attributes Constant and Protected,
NumericQ[E] is True, and D[E, x] is 0. N[E, prec] evaluates it to any
precision.

Examples

No verified examples yet for this function.

Implementation notes

  • Attributes Constant, Protected. Attributes[E] = {Constant, Protected};

Attributes: Constant, Protected.

Implementation status

Stable — documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

References

Notes & additional examples

Worked examples

In[1]:= Log[E^3]
Out[1]= 3

In[1]:= N[E, 40]
Out[1]= 2.7182818284590452353602874713526624977572

In[1]:= Sum[1/n!, {n, 0, Infinity}]
Out[1]= E

In[1]:= Limit[(1 + 1/n)^n, n -> Infinity]
Out[1]= E

Notes

E is the exponential constant e, the base of the natural logarithm. It is a protected Constant, so D[E, x] is 0 and it survives evaluation symbolically until N is applied — N[E, prec] returns it to any requested precision via the MPFR backend. The constant is recognised by the rest of the system, so the classic limit and series characterisations of e both fold back to E, and Log[E^3] simplifies to its exponent.