Question

Can the graph of $\tan^{-1}{\left(\frac{\sin x}{x}\right)}$ be expressed as $Ce^{-kx}\cos(\omega x + \phi)$?

score 117 · Answer 1 · 2026-04-15 22:39:05

117

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Can the graph of $\tan^{-1}{\left(\frac{\sin x}{x}\right)}$ be expressed as $Ce^{-kx}\cos(\omega x + \phi)$?

Published on 15 Apr 2026 - 22:39

score 50 · Answer 2 · 2026-04-13 17:47:41

50

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How can I get a closed form for $\sum_{k=1}^C \dfrac 1 k e^{-k} $?

Published on 13 Apr 2026 - 17:47

score 116 · Answer 3 · 2026-04-12 22:24:48

116

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Integral with the exponential function

Published on 12 Apr 2026 - 22:24

score 33.4k · Answer 4 · 2026-04-14 02:56:20

33.4k

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How does $e^{-j\pi n}$ become $(-1)^n$

Published on 14 Apr 2026 - 2:56

score 213 · Answer 5 · 2026-04-14 15:39:52

213

Views

what is the region of convergence of this exponential?

Published on 14 Apr 2026 - 15:39

score 67 · Answer 6 · 2026-04-11 06:13:50

67

Views

Proving an inequality involving logarithms in two dimensions

Published on 11 Apr 2026 - 6:13

score 207 · Answer 7 · 2026-04-16 09:35:56

207

Views

$e$ is the only number in the universe having this property?

Published on 16 Apr 2026 - 9:35

score 101 · Answer 8 · 2026-04-13 10:51:19

101

Views

What will be Summation $\sum_{n=1}^{\infty}\frac{n^2}{n!}$

Published on 13 Apr 2026 - 10:51

score 63 · Answer 9 · 2026-04-14 03:35:15

63

Views

How to verify the equation $\frac{1}{e^{2\pi x} - 1} = \sum_{k = 1}^{\infty} e^{-2\pi kx}$

Published on 14 Apr 2026 - 3:35

score 190 · Answer 10 · 2026-04-13 00:22:10

190

Views

The sum of power series with denominators $n!(n+1)!$

Published on 13 Apr 2026 - 0:22

score 797 · Answer 11 · 2026-04-09 14:35:06

797

Views

Solving a quadratic equation involving e

Published on 09 Apr 2026 - 14:35

score 48 · Answer 12 · 2026-04-14 17:11:35

48

Views

Can $x$ be defined without itself when $\frac{p^{x}}{x} = c$?

Published on 14 Apr 2026 - 17:11

score 25 · Answer 13 · 2026-03-27 10:12:54

25

Views

Finding suitable $x:[-T,T]\to\mathbb{R}^n, A\in\mathbb{R}^{n\times n}$ such that $x'(t) = Ax(t)$ when $\frac{d^2}{dt^2}B(t)=B(t)$

Published on 27 Mar 2026 - 10:12

score 342 · Answer 14 · 2026-04-15 06:30:30

342

Views

Closed form or upper bound for $\lim_{n\to\infty}\sum_{k=0}^n\frac{e^{-k^2x}-e^{-(k+1)^2x}}{2k+1} $?

Published on 15 Apr 2026 - 6:30

score 90 · Answer 15 · 2026-04-16 04:46:58

90

Views

Complex-valued functions with value and derivatives having absolute less than 1 everywhere: Does $f(0)=|f'(0)|=1$ imply $f(t)=e^{\pm it}$?

Published on 16 Apr 2026 - 4:46

List Question

Can the graph of $\tan^{-1}{\left(\frac{\sin x}{x}\right)}$ be expressed as $Ce^{-kx}\cos(\omega x + \phi)$?

How can I get a closed form for $\sum_{k=1}^C \dfrac 1 k e^{-k} $?

Integral with the exponential function

How does $e^{-j\pi n}$ become $(-1)^n$

what is the region of convergence of this exponential?

Proving an inequality involving logarithms in two dimensions

$e$ is the only number in the universe having this property?

What will be Summation $\sum_{n=1}^{\infty}\frac{n^2}{n!}$

How to verify the equation $\frac{1}{e^{2\pi x} - 1} = \sum_{k = 1}^{\infty} e^{-2\pi kx}$

The sum of power series with denominators $n!(n+1)!$

Solving a quadratic equation involving e

Can $x$ be defined without itself when $\frac{p^{x}}{x} = c$?

Finding suitable $x:[-T,T]\to\mathbb{R}^n, A\in\mathbb{R}^{n\times n}$ such that $x'(t) = Ax(t)$ when $\frac{d^2}{dt^2}B(t)=B(t)$

Closed form or upper bound for $\lim_{n\to\infty}\sum_{k=0}^n\frac{e^{-k^2x}-e^{-(k+1)^2x}}{2k+1} $?

Complex-valued functions with value and derivatives having absolute less than 1 everywhere: Does $f(0)=|f'(0)|=1$ imply $f(t)=e^{\pm it}$?

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