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Консультация № 185872
21.04.2012, 22:58
114.74 руб.
0
2
2
Здравствуйте! У меня возникли сложности с таким вопросом:
Найти все разложения заданных функций по степеням заданной разности.Указать области пригодности каждого из разложений:
1)
2)
Заранее благодарен за помощь!
Найти все разложения заданных функций по степеням заданной разности.Указать области пригодности каждого из разложений:
1)
2)
Заранее благодарен за помощь!
Обсуждение
21.04.2012, 23:55
общий
это ответ
Здравствуйте, G-buck!
1.
.
,
где
, n чётное,
, n нечётное
(расписали ряд для косинуса и синуса).
Т.о.
,
где cn описаны выше.
Ряд сходится во всех точках, кроме
.
1.
.,где
, n чётное,, n нечётное(расписали ряд для косинуса и синуса).
Т.о.
,где cn описаны выше.
Ряд сходится во всех точках, кроме
.
22.04.2012, 23:33
общий
это ответ
Здравствуйте, G-buck!
2)
Особыми точками f(z) являются z1=-1, z2=1, z3=[$8734$].
Запишем разложение в окрестности точки z1=-1. Расстояние до ближайшей особой точки z2=1 равно 2. Поэтому разложение будет пригодно в кольце 0<|z+1|<2 .
Разложим дроби 1/(z-1)2, 1/(z-1)3 в ряды по степеням z+1.
Используя почленное дифференцирование ряда, находим
Следовательно,
или
2)
Особыми точками f(z) являются z1=-1, z2=1, z3=[$8734$].
Запишем разложение в окрестности точки z1=-1. Расстояние до ближайшей особой точки z2=1 равно 2. Поэтому разложение будет пригодно в кольце 0<|z+1|<2 .
Разложим дроби 1/(z-1)2, 1/(z-1)3 в ряды по степеням z+1.
Используя почленное дифференцирование ряда, находим
Следовательно,
или
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