Question

How to write this series as a ratio of polynomials?

score 92 · Answer 1 · 2026-04-12 23:26:25

92

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How to write this series as a ratio of polynomials?

Published on 12 Apr 2026 - 23:26

score 150 · Answer 2 · 2020-07-07 16:28:55

150

Views

Is the radius of convergence related to the ratio limit or half of the interval of convergence?

Published on 07 Jul 2020 - 16:28

score 94 · Answer 3 · 2026-03-28 23:27:20

94

Views

Finding the Laurent Series of $f(z)=\displaystyle\frac{z^2 e^{1/z}}{z-1}$ for $0<|z|<1$

Published on 28 Mar 2026 - 23:27

score 114 · Answer 4 · 2026-04-10 12:06:32

114

Views

How to prove the Taylor series converges for a smooth function with nonnegative derivatives?

Published on 10 Apr 2026 - 12:06

score 897 · Answer 5 · 2026-04-09 15:45:42

897

Views

How to find a power series for a given function?

Published on 09 Apr 2026 - 15:45

score 39 · Answer 6 · 2020-07-08 07:35:56

39

Views

Limits:my question is why can't the numerator be equal to $1/4$ as it forms Grandi Series?

Published on 08 Jul 2020 - 7:35

score 42 · Answer 7 · 2020-07-08 10:06:37

42

Views

Write this integral as a power series

Published on 08 Jul 2020 - 10:06

score 39 · Answer 8 · 2026-04-11 16:51:15

39

Views

Find a closed form of this power series f(x).

Published on 11 Apr 2026 - 16:51

score 482 · Answer 9 · 2020-07-09 16:22:27

482

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Suppose that $f$ is an entire function satisfying $f(2z)=\frac{f(z)+f(z+1)}{2}$. Show that $f$ is constant.

Published on 09 Jul 2020 - 16:22

score 3.1k · Answer 10 · 2026-04-11 16:50:21

3.1k

Views

Generalisation of $\log(1-x)$ expansion?

Published on 11 Apr 2026 - 16:50

score 1.1k · Answer 11 · 2026-04-06 17:51:47

1.1k

Views

Show that the power series $\sum_{n=0}^\infty \frac{z^n}{n!}$ converges uniformly for all $z$.

Published on 06 Apr 2026 - 17:51

score 145 · Answer 12 · 2026-04-02 13:42:50

145

Views

If we pick a sequence of numbers $(a_k)$ at random, what is the expected radius of convergence of $\sum_k a_k x^k$?

Published on 02 Apr 2026 - 13:42

score 114 · Answer 13 · 2020-07-10 08:06:56

114

Views

Evaluating $ \lim_{x \to 0}\left(-\frac{1}{3 !}+\frac{x^{2}}{5 !}-\frac{x^{4}}{7 !}+\frac{x^{6}}{9!}+\cdots\right) $

Published on 10 Jul 2020 - 8:06

score 126 · Answer 14 · 2026-04-12 00:15:54

126

Views

Stuck with integrals

Published on 12 Apr 2026 - 0:15

score 89 · Answer 15 · 2026-03-26 11:01:17

89

Views

Prove: if $\sum^\infty_{n=0}a_nx^n$ converges for every $x$, then $\sum^\infty_{n=0}a_n$ converges absolutely

Published on 26 Mar 2026 - 11:01

List Question

How to write this series as a ratio of polynomials?

Is the radius of convergence related to the ratio limit or half of the interval of convergence?

Finding the Laurent Series of $f(z)=\displaystyle\frac{z^2 e^{1/z}}{z-1}$ for $0<|z|<1$

How to prove the Taylor series converges for a smooth function with nonnegative derivatives?

How to find a power series for a given function?

Limits:my question is why can't the numerator be equal to $1/4$ as it forms Grandi Series?

Write this integral as a power series

Find a closed form of this power series f(x).

Suppose that $f$ is an entire function satisfying $f(2z)=\frac{f(z)+f(z+1)}{2}$. Show that $f$ is constant.

Generalisation of $\log(1-x)$ expansion?

Show that the power series $\sum_{n=0}^\infty \frac{z^n}{n!}$ converges uniformly for all $z$.

If we pick a sequence of numbers $(a_k)$ at random, what is the expected radius of convergence of $\sum_k a_k x^k$?

Evaluating $ \lim_{x \to 0}\left(-\frac{1}{3 !}+\frac{x^{2}}{5 !}-\frac{x^{4}}{7 !}+\frac{x^{6}}{9!}+\cdots\right) $

Stuck with integrals

Prove: if $\sum^\infty_{n=0}a_nx^n$ converges for every $x$, then $\sum^\infty_{n=0}a_n$ converges absolutely

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