Definition:Euler's Number/Limit of Series
< Definition:Euler's Number(Redirected from Definition:Factorial Series)
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Definition
The series $\ds \sum_{n \mathop = 0}^\infty \frac 1 {n!}$ converges to a limit.
This limit is Euler's number $e$.
Decimal Expansion
The decimal expansion of Euler's number $e$ starts:
- $2 \cdotp 71828 \, 18284 \, 59045 \, 23536 \, 02874 \, 71352 \, 66249 \, 77572 \, 47093 \, 69995 \ldots$
Also known as
The expression for Euler's number $e$ as the limit of the series:
- $\ds \sum_{n \mathop = 0}^\infty \frac 1 {n!}$
is known as the factorial series.
Also see
Source of Name
This entry was named for Leonhard Paul Euler.
Sources
- 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $1$: Review of some real analysis: $\S 1.2$: Real Sequences
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $2 \cdotp 718 \, 281 \, 828 \, 459 \, 045 \, 235 \, 360 \, 287 \, 471 \, 352 \, 662 \, 497 \, 757 \, 247 \, 093 \, 699 \ldots$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2 \cdotp 71828 \, 18284 \, 59045 \, 23536 \, 02874 \, 71352 \, 66249 \, 77572 \, 47093 \, 69995 \ \ldots$
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): e
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): factorial series
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): e
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): factorial series