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Консультация № 178650
26.05.2010, 01:16
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Помогите решить пожалуйста!!!!
Найти аналитическую функцию f (z). если известна ее вещественная или мнимая часть и значение функции в заданной точке
U (x.y) = (x *cosy - y* siny) е^x + 1; f(0) =1
Заранее спасибо!!!!
Найти аналитическую функцию f (z). если известна ее вещественная или мнимая часть и значение функции в заданной точке
U (x.y) = (x *cosy - y* siny) е^x + 1; f(0) =1
Заранее спасибо!!!!
Обсуждение
26.08.2022, 11:15
общий
это ответ
Здравствуйте, Юрий Николаевич!
1. Определим мнимую часть
функции 
Имеем
Согласно условиям Коши -- Римана (необходимым условиям дифференцируемости) для функции
должны выполняться равенства 
Тогда
(постоянные интегрирования опускаем) 
где
-- неизвестная функция, зависящая только от 
с другой стороны, как указано выше, поэтому 
Следовательно,
2. Определим искомую функцию Имеем
Поскольку
постольку
Значит,
Ответ:
1. Определим мнимую часть
функции ИмеемСогласно условиям Коши -- Римана (необходимым условиям дифференцируемости) для функции
должны выполняться равенства Тогда (постоянные интегрирования опускаем) где
-- неизвестная функция, зависящая только от с другой стороны, как указано выше,
поэтому Следовательно,2. Определим искомую функцию
ИмеемПоскольку
постолькуЗначит,
Ответ:
Об авторе:
Facta loquuntur.
Facta loquuntur.
Форма ответа
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