Question

How can one prove the impossibility of writing $ \int e^{x^{2}} \, \mathrm{d}{x} $ in terms of elementary functions?

score 1.4k · Answer 1 · 2026-04-11 16:37:31

1.4k

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How can one prove the impossibility of writing $ \int e^{x^{2}} \, \mathrm{d}{x} $ in terms of elementary functions?

Published on 11 Apr 2026 - 16:37

score 214 · Answer 2 · 2026-05-10 21:26:56

214

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Need an equation to fit this exponential curve

Published on 10 May 2026 - 21:26

score 13.3k · Answer 3 · 2026-04-11 20:26:52

13.3k

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Prove that the limit definition of the exponential function implies its infinite series definition.

Published on 11 Apr 2026 - 20:26

score 62 · Answer 4 · 2026-04-11 00:07:39

62

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How to solve this equation with linear n as well as polynomial n?

Published on 11 Apr 2026 - 0:07

score 60.6k · Answer 5 · 2026-04-13 19:09:18

60.6k

Views

Integrate $e^{-ax}$ and $xe^{-ax}$?

Published on 13 Apr 2026 - 19:09

score 164 · Answer 6 · 2026-04-14 00:55:55

164

Views

Why is $3^n$ not in $\Theta(2^n)$

Published on 14 Apr 2026 - 0:55

score 2.6k · Answer 7 · 2026-04-15 06:02:02

2.6k

Views

Why is $\det(e^X)=e^{\operatorname{tr}(X)}$?

Published on 15 Apr 2026 - 6:02

score 85 · Answer 8 · 2026-04-14 05:17:02

85

Views

Exponential equations solving methods?

Published on 14 Apr 2026 - 5:17

score 33 · Answer 9 · 2026-04-14 02:10:46

33

Views

Particular solutions for a linear 2nd order ODE

Published on 14 Apr 2026 - 2:10

score 316 · Answer 10 · 2026-04-12 08:27:51

316

Views

How to show limit containing exp and cos series inside?

Published on 12 Apr 2026 - 8:27

score 1.3k · Answer 11 · 2026-04-12 04:42:50

1.3k

Views

What is the limit of $\mathrm{e}^{At}$ when $t\to \infty$, for $A$ a square matrix?

Published on 12 Apr 2026 - 4:42

score 85 · Answer 12 · 2026-04-14 18:37:48

85

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How to prove that if $\int_t^\infty(s-t-\frac{1}{\lambda})\,f(s)\ ds =0$ for all $t\ge 0$ then $f(s)=\lambda\, \mathrm{e}^{-\lambda s}$

Published on 14 Apr 2026 - 18:37

score 1k · Answer 13 · 2026-04-11 05:00:14

1k

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Creating a custom exponential function

Published on 11 Apr 2026 - 5:00

score 98 · Answer 14 · 2026-04-17 08:55:16

98

Views

Noncircular construction of $e$ and $\ln$ for the real line

Published on 17 Apr 2026 - 8:55

score 92 · Answer 15 · 2026-04-08 16:42:32

92

Views

How can I solve the equation...

Published on 08 Apr 2026 - 16:42

List Question

How can one prove the impossibility of writing $ \int e^{x^{2}} \, \mathrm{d}{x} $ in terms of elementary functions?

Need an equation to fit this exponential curve

Prove that the limit definition of the exponential function implies its infinite series definition.

How to solve this equation with linear n as well as polynomial n?

Integrate $e^{-ax}$ and $xe^{-ax}$?

Why is $3^n$ not in $\Theta(2^n)$

Why is $\det(e^X)=e^{\operatorname{tr}(X)}$?

Exponential equations solving methods?

Particular solutions for a linear 2nd order ODE

How to show limit containing exp and cos series inside?

What is the limit of $\mathrm{e}^{At}$ when $t\to \infty$, for $A$ a square matrix?

How to prove that if $\int_t^\infty(s-t-\frac{1}{\lambda})\,f(s)\ ds =0$ for all $t\ge 0$ then $f(s)=\lambda\, \mathrm{e}^{-\lambda s}$

Creating a custom exponential function

Noncircular construction of $e$ and $\ln$ for the real line

How can I solve the equation...

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