be under the impression

think believe feel reckon be under the impression be of the opinion

These words all mean to have an idea that sth is true or possible or to have a particular opinion about sb/sth.以上各词均含以为、认为之义。

to have an idea that sth is true or possible, although you are not completely certain; to have a particular opinion about sb/sth指以为、认为某人／事物…，但不肯定：

Do you think (that) they'll come?

你认为他们会来吗？

Well, I like it. What do you think?

嗯，我喜欢这个。你认为怎么样？

to have an idea that sth is true or possible, although you are not completely certain; to have a particular opinion about sb/sth指以为、认为某人／事物…，但不肯定：

Police believe (that) the man may be armed.

警方认为那个人可能携有武器。


When you are expressing an idea that you have or that sb has of what is true or possible, believe is more formal than think . It is used especially for talking about ideas that other people have; think is used more often for talking about your own ideas.
When you are expressing an opinion, believe is stronger than think and is used especially for matters of principle; think is used more for practical matters or matters of personal taste.

to have a particular opinion about sth that has happened or about what you/sb ought to do指认为（已发生的事情…）、相信（应该…）：

We all felt (that) we were unlucky to lose.

我们都认为输了是运气不好。

( informal ) to think that sth is true or possible指认为、以为：

I reckon (that) I'm going to get that job.

我认为我会得到那份工作。

to have an idea that sth is true指以为某事…：

I was under the impression that the work had already been completed.

我还以为已经完工了呢。

( formal ) to believe or think that…指相信、认为：

We are of the opinion that great caution should be exercised in dealing with this matter.

我们认为处理这事应该非常谨慎。

1

Whoever wrote this remark seems to be under the impression that the point of being at Yale is to spend $ 40,000 a year of your parents'money and get away with learning as little as possible .

无论谁写的这条评论都被带怀有这种印象，那就是每年花费你父母四万美金在耶鲁上，学并尽可能少的学到知识。
2

Many applicants , whether they are repeat or first-time applicants , may be under the mistaken impression that Consular Officers only reluctantly issue visas .

在很多申请人中，无论是返签还是首签的申请人，他们也许会有一个错误的印象就是领事官员只会给他们拒签。