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Консультация № 199917
19.12.2020, 15:31
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Разложить функцию в ряд Фурье: f(x)=|x|/x заданную на промежутке xє(-1;0) U (0,1)
Построить график суммы ряда
Разложить функцию в ряд Фурье: f(x)=|x|/x заданную на промежутке xє(-1;0) U (0,1)
Построить график суммы ряда
Обсуждение
25.12.2020, 15:30
общий
это ответ
Здравствуйте, iranisimova36@gmail.com!
Из условия задачи следует, что функция f(x) имеет вид
и задана на интервале (-1, 1).
В общем случае периодическая функция y с периодом 2l разлагается на интервале (a, b) (b - a = 2l) в ряд Фурье вида
где коэффициенты a[sub]n[/sub], b[sub]n[/sub] равны
В данном случае = -1, b = 1, l = 1 и коэффициенты будут равны
Таким образом, ряд Фурье для данной функции будет содержать только члены с синусами, причём
то есть
Из условия задачи следует, что функция f(x) имеет вид
и задана на интервале (-1, 1).
В общем случае периодическая функция y с периодом 2l разлагается на интервале (a, b) (b - a = 2l) в ряд Фурье вида
где коэффициенты a[sub]n[/sub], b[sub]n[/sub] равны
В данном случае = -1, b = 1, l = 1 и коэффициенты будут равны
Таким образом, ряд Фурье для данной функции будет содержать только члены с синусами, причём
то есть
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