Добавил:
Upload
Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз:
Предмет:
Файл:421 FunSeries.docx
2.12. Euler’s formula
We
define the function
of the complex variable
by the formula:
Let
now
,
where
,
be a real number, and
the imaginary unit
.
Then from the formula (2.4) we have:
Where
we have used the Taylor’s series for
and
.
Thus,
we have obtained the formula:
,
which is called Euler’s formula.
Example
2.18.
Compute
By Euler’s formula, we have
,
