q*****z
发帖数: 191 | 1 Hi,
I have been thinking about the question of how to use ratio test to estimate
the radius of convergence of a power series when it only has even or odd
terms. For example, I have a complicated power series f(x):
f(x) = 1+f2*x^2+f4*x^4+...
To do a ratio test, estimate the following limit:
lim(fn/fn+2)
Then the value obtained is radio of convergence, but is it r or r^2? The
unit matches with r^2 but I haven't seen such things anywhere.
Thanks. | n*******l
发帖数: 2911 | 2 大一的学生也来BBS了？ 先看看书，弄明白什么是radius of convergence吧。
estimate
【在 q*****z 的大作中提到】
: Hi,
: I have been thinking about the question of how to use ratio test to estimate
: the radius of convergence of a power series when it only has even or odd
: terms. For example, I have a complicated power series f(x):
: f(x) = 1+f2*x^2+f4*x^4+...
: To do a ratio test, estimate the following limit:
: lim(fn/fn+2)
: Then the value obtained is radio of convergence, but is it r or r^2? The
: unit matches with r^2 but I haven't seen such things anywhere.
: Thanks.
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