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Консультация № 199933
20.12.2020, 13:12
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Здравствуйте! Прошу помощи в следующем вопросе:Помогите пожалуйста фотка в закрепе
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Обсуждение
25.12.2020, 12:57
общий
это ответ
Здравствуйте, zhalykov.2015!
По теореме Коши для функции f(z), аналитической во всех точках контура Г и внутри контура, за исключением особых точек z[sub]1[/sub],... z[sub]n[/sub], интеграл по контуру определяется выражением
где Res f(z[sub]k[/sub]) - вычет в особой точке z[sub]k[/sub]. Для полюса кратности n вычет может быть вычислен по формуле:
В частности, для простого полюса (n=1) вычет равен
В данном случае подинтегральная функция
имеет две особые точки кратности 1 (z = 7 и z = -5), лежащие внутри контура Г: |z|=36, представляющего собой окружность радиуса 36 (не 6!) на комплексной плоскости. Найдём вычеты для этих точек:
Тогда
По теореме Коши для функции f(z), аналитической во всех точках контура Г и внутри контура, за исключением особых точек z[sub]1[/sub],... z[sub]n[/sub], интеграл по контуру определяется выражением
где Res f(z[sub]k[/sub]) - вычет в особой точке z[sub]k[/sub]. Для полюса кратности n вычет может быть вычислен по формуле:
В частности, для простого полюса (n=1) вычет равен
В данном случае подинтегральная функция
имеет две особые точки кратности 1 (z = 7 и z = -5), лежащие внутри контура Г: |z|=36, представляющего собой окружность радиуса 36 (не 6!) на комплексной плоскости. Найдём вычеты для этих точек:
Тогда
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