Question

An inequality involving recurrence sequence $b_{n+1}=\frac{b_{n}^{2}+2b_{n}}{b_{n}^{2}+2b_{n}+2}$ with $b_{1}=1$ and still unsolved

score 78 · Answer 1 · 2021-02-14 08:40:44

78

Views

An inequality involving recurrence sequence $b_{n+1}=\frac{b_{n}^{2}+2b_{n}}{b_{n}^{2}+2b_{n}+2}$ with $b_{1}=1$ and still unsolved

Published on 14 Feb 2021 - 8:40

score 546 · Answer 2 · 2021-02-15 07:05:52

546

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The variation of a Ukrainian Olympiad problem: 10982

Published on 15 Feb 2021 - 7:05

score 75 · Answer 3 · 2021-02-16 07:45:07

75

Views

Find the $o\left ( 1 \right )$ so that $2b_{n+ 1}\sim b_{n}^{2}+ o\left ( 1 \right )$

Published on 16 Feb 2021 - 7:45

score 49 · Answer 4 · 2021-02-17 09:27:32

49

Views

Find $\mathcal{O}_{\mathscr{L}(a)}$ so that $a_n\sim\sqrt{1+\frac{1}{1+a_n}}+\mathcal{O}_{\mathscr{L}(a)}(\frac{1}{n})\,{\rm as}\,n\rightarrow\infty$

Published on 17 Feb 2021 - 9:27

score 101 · Answer 5 · 2021-02-18 03:51:16

101

Views

Find the Taylor and Laurent series with center at $z_{o}= 1$ of the function $\frac{\sinh(z)}{(z-1)^4}$

Published on 18 Feb 2021 - 3:51

score 180 · Answer 6 · 2021-02-19 11:57:56

180

Views

Uniform convergence to swap summation and integration

Published on 19 Feb 2021 - 11:57

score 1.1k · Answer 7 · 2021-02-19 13:00:35

1.1k

Views

Find the Laurent expansion of $(1-z)e^{1/z}$ - When can we use Taylor series to find Laurent series?

Published on 19 Feb 2021 - 13:00

score 394 · Answer 8 · 2026-03-29 15:59:52

394

Views

Determining poles and their orders without using Laurent series

Published on 29 Mar 2026 - 15:59

score 72 · Answer 9 · 2021-02-23 09:52:19

72

Views

Given a recursion $\frac{a_{n+1}}{4a_{n+1}+n+1}=\frac{2(a_n+n)^2}{9n(4a_n+n)}$ with $a_1=1.$ Show that $a_n\sim\frac n2\,{\rm as}\,n\rightarrow\infty$

Published on 23 Feb 2021 - 9:52

score 369 · Answer 10 · 2026-03-27 19:15:30

369

Views

Find a value of $\;\lim\limits_{n\rightarrow\infty}n\left ( e- e^{\frac{1}{e}}\uparrow\uparrow n \right )$

Published on 27 Mar 2026 - 19:15

score 209 · Answer 11 · 2026-03-31 09:22:18

209

Views

Laurent series and Weierstrass zeta function

Published on 31 Mar 2026 - 9:22

score 48 · Answer 12 · 2021-03-03 22:00:17

48

Views

Question About Laurent Series and Expanding about Infinity

Published on 03 Mar 2021 - 22:00

score 59 · Answer 13 · 2021-03-09 00:01:03

59

Views

A question about multiplying Laurent series

Published on 09 Mar 2021 - 0:01

score 80 · Answer 14 · 2021-03-13 09:53:01

80

Views

I want to know if the Laurent series for $(e ^ z/ z) + e ^ {1 / z}$ is resolved correctly

Published on 13 Mar 2021 - 9:53

score 68 · Answer 15 · 2021-03-16 01:30:03

68

Views

Understanding finding the Laurent series

Published on 16 Mar 2021 - 1:30

List Question

An inequality involving recurrence sequence $b_{n+1}=\frac{b_{n}^{2}+2b_{n}}{b_{n}^{2}+2b_{n}+2}$ with $b_{1}=1$ and still unsolved

The variation of a Ukrainian Olympiad problem: 10982

Find the $o\left ( 1 \right )$ so that $2b_{n+ 1}\sim b_{n}^{2}+ o\left ( 1 \right )$

Find $\mathcal{O}_{\mathscr{L}(a)}$ so that $a_n\sim\sqrt{1+\frac{1}{1+a_n}}+\mathcal{O}_{\mathscr{L}(a)}(\frac{1}{n})\,{\rm as}\,n\rightarrow\infty$

Find the Taylor and Laurent series with center at $z_{o}= 1$ of the function $\frac{\sinh(z)}{(z-1)^4}$

Uniform convergence to swap summation and integration

Find the Laurent expansion of $(1-z)e^{1/z}$ - When can we use Taylor series to find Laurent series?

Determining poles and their orders without using Laurent series

Given a recursion $\frac{a_{n+1}}{4a_{n+1}+n+1}=\frac{2(a_n+n)^2}{9n(4a_n+n)}$ with $a_1=1.$ Show that $a_n\sim\frac n2\,{\rm as}\,n\rightarrow\infty$

Find a value of $\;\lim\limits_{n\rightarrow\infty}n\left ( e- e^{\frac{1}{e}}\uparrow\uparrow n \right )$

Laurent series and Weierstrass zeta function

Question About Laurent Series and Expanding about Infinity

A question about multiplying Laurent series

I want to know if the Laurent series for $(e ^ z/ z) + e ^ {1 / z}$ is resolved correctly

Understanding finding the Laurent series

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