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Консультация № 196963
05.11.2019, 10:27
0.00 руб.
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Помогите пожалуйста
Установить является ли функция w=f(z) аналитической
Помогите пожалуйста
Установить является ли функция w=f(z) аналитической
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Обсуждение
09.11.2019, 11:32
общий
это ответ
Здравствуйте, Елена!
Необходимым и достаточным условием аналитичности функции f(z) = f(x+iy) = u(x,y) + iv(x,y) является непрерывность частных производных первого порядка
и выполнение условия Коши-Римана:
В данном случае
то есть u(x, y) = 8x, v(x, y) = 2y. Так как
- непрерывные функции и
но
то функция f(x) не является аналитической.
Необходимым и достаточным условием аналитичности функции f(z) = f(x+iy) = u(x,y) + iv(x,y) является непрерывность частных производных первого порядка
и выполнение условия Коши-Римана:
В данном случае
то есть u(x, y) = 8x, v(x, y) = 2y. Так как
- непрерывные функции и
но
то функция f(x) не является аналитической.
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