Question

How to invert an arithmetic function where Möbius inversion may not apply?

score 57 · Answer 1 · 2026-03-23 10:12:43

57

Views

How to invert an arithmetic function where Möbius inversion may not apply?

Published on 23 Mar 2026 - 10:12

score 307 · Answer 2 · 2018-11-08 12:45:07

307

Views

Sum of infinite power series with factorial

Published on 08 Nov 2018 - 12:45

score 187 · Answer 3 · 2018-11-08 13:01:14

187

Views

Is the power series ring over a polynomial ring the same as the polynomial ring over the power series ring?

Published on 08 Nov 2018 - 13:01

score 82 · Answer 4 · 2026-03-25 12:52:40

82

Views

Express a complex analytic function as a single power series

Published on 25 Mar 2026 - 12:52

score 49 · Answer 5 · 2018-11-08 20:32:39

49

Views

Prove that $\frac{t^{x-1}}{1+t^y} = \sum_{n=0}^{\infty} (-1)^nt^{x-1+yn}$.

Published on 08 Nov 2018 - 20:32

score 70 · Answer 6 · 2026-03-26 04:14:37

70

Views

Show that $\sum_{n=1}^{\infty} nx^n/(n-1)! = e^xx(x+1)$

Published on 26 Mar 2026 - 4:14

score 39 · Answer 7 · 2026-03-27 01:46:07

39

Views

Neumann expansion of seemingly simple series

Published on 27 Mar 2026 - 1:46

score 44 · Answer 8 · 2018-11-10 22:21:08

44

Views

Finding the series expansion of $\frac{1}{z-b}$ around $a$

Published on 10 Nov 2018 - 22:21

score 327 · Answer 9 · 2018-11-12 03:28:59

327

Views

Finding the radius of convergence of $\sum_{n=0}^{\infty} 3^{n} \cdot x^{2n}$

Published on 12 Nov 2018 - 3:28

score 66 · Answer 10 · 2018-11-12 07:41:45

66

Views

If $f(x) = xe^{-x^2}$, how many Taylor series terms are necessary to ensure our approximation of $f(1)$ is within $10^{-6}$?

Published on 12 Nov 2018 - 7:41

score 71 · Answer 11 · 2026-03-27 03:44:13

71

Views

Radius of convergence of power series $\sum_{n=1}^{\infty}\frac{1}{(1+\frac{1}{n})^{n^2}}x^{6n+2}$

Published on 27 Mar 2026 - 3:44

score 70 · Answer 12 · 2018-11-12 17:05:26

70

Views

Finding the radius of convergence for $\frac{1}{(3 - x)(1 + x)^{2}}$ at $x_{0} = 0$ and $x_{0} = 1$

Published on 12 Nov 2018 - 17:05

score 166 · Answer 13 · 2026-03-25 01:18:57

166

Views

Find the sum of $1-\frac17+\frac19-\frac1{15}+\frac1{17}-\frac1{23}+\frac1{25}-\dots$

Published on 25 Mar 2026 - 1:18

score 88 · Answer 14 · 2018-11-13 13:27:50

88

Views

Taylor series of $\frac{2e^x}{e^{2x}+1}$

Published on 13 Nov 2018 - 13:27

score 90 · Answer 15 · 2018-11-13 22:30:52

90

Views

For what $x>0$ series $\sum_{n=1}^{\infty} x^{1+\frac{1}{\sqrt2}+\frac{1}{\sqrt3}...+\frac{1}{\sqrt n}}$ is convergent?

Published on 13 Nov 2018 - 22:30

List Question

How to invert an arithmetic function where Möbius inversion may not apply?

Sum of infinite power series with factorial

Is the power series ring over a polynomial ring the same as the polynomial ring over the power series ring?

Express a complex analytic function as a single power series

Prove that $\frac{t^{x-1}}{1+t^y} = \sum_{n=0}^{\infty} (-1)^nt^{x-1+yn}$.

Show that $\sum_{n=1}^{\infty} nx^n/(n-1)! = e^xx(x+1)$

Neumann expansion of seemingly simple series

Finding the series expansion of $\frac{1}{z-b}$ around $a$

Finding the radius of convergence of $\sum_{n=0}^{\infty} 3^{n} \cdot x^{2n}$

If $f(x) = xe^{-x^2}$, how many Taylor series terms are necessary to ensure our approximation of $f(1)$ is within $10^{-6}$?

Radius of convergence of power series $\sum_{n=1}^{\infty}\frac{1}{(1+\frac{1}{n})^{n^2}}x^{6n+2}$

Finding the radius of convergence for $\frac{1}{(3 - x)(1 + x)^{2}}$ at $x_{0} = 0$ and $x_{0} = 1$

Find the sum of $1-\frac17+\frac19-\frac1{15}+\frac1{17}-\frac1{23}+\frac1{25}-\dots$

Taylor series of $\frac{2e^x}{e^{2x}+1}$

For what $x>0$ series $\sum_{n=1}^{\infty} x^{1+\frac{1}{\sqrt2}+\frac{1}{\sqrt3}...+\frac{1}{\sqrt n}}$ is convergent?

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