Question

Is the function $f(x)=\frac{\left(1-x^2+\sqrt{\left(1-x^2\right)^2}\right)}{2}e^{-\frac{x^2}{1-x^2}}$ a bump-function $\in C_c^\infty$? Diff. Eq.?

score 510 · Answer 1 · 2026-04-26 00:08:21

510

Views

Is the function $f(x)=\frac{\left(1-x^2+\sqrt{\left(1-x^2\right)^2}\right)}{2}e^{-\frac{x^2}{1-x^2}}$ a bump-function $\in C_c^\infty$? Diff. Eq.?

Published on 26 Apr 2026 - 0:08

score 191 · Answer 2 · 2026-04-12 21:11:42

191

Views

Are these functions Absolute Continuous? (continuous nowhere-differentiable functions)

Published on 12 Apr 2026 - 21:11

score 1.6k · Answer 3 · 2026-04-16 19:39:10

1.6k

Views

Is each of $\int_0^\infty\frac{dx}{x^x},\int_0^\infty\frac{dx}{x^{x^{x^x}}},\int_0^\infty\frac{dx}{x^{x^{x^{x^{x^x}}}}},\cdots$ less than $2$?

Published on 16 Apr 2026 - 19:39

score 64 · Answer 4 · 2026-04-14 13:34:39

64

Views

Expressing an exponential with a sum of mathieu functions

Published on 14 Apr 2026 - 13:34

score 142 · Answer 5 · 2026-04-15 18:05:27

142

Views

Asymptotic expression around $x=\infty$ of Infinite sum of the exponential integral: $\sum_{i=1,3,5..}\text{Ei}\left(\frac{-i^2 \pi^3}{4 x^2}\right)$

Published on 15 Apr 2026 - 18:05

score 216 · Answer 6 · 2026-04-15 20:29:58

216

Views

Proving $48\sum\limits_{n\ge1}{e^{2n}(1+e^{4n})\over(1-e^{4n})^2}=24\pi^2\sum\limits_{n\ge1}{e^{\pi^2n}(1+e^{2\pi^2n})\over(1-e^{2\pi^2n})^2}+\pi^2-2$

Published on 15 Apr 2026 - 20:29

score 100 · Answer 7 · 2026-04-08 12:34:01

100

Views

Asymptotics of an integral involving a Bessel function does not yield expected result

Published on 08 Apr 2026 - 12:34

score 824 · Answer 8 · 2026-04-16 21:30:55

824

Views

Why Dottie$=2\sqrt{I^{-1}_\frac12(\frac 12,\frac 32)-I^{-1}_\frac12(\frac 12,\frac 32)^2} = \sin^{-1}\big(1-2I^{-1}_\frac12(\frac 12,\frac 32)\big)$?

Published on 16 Apr 2026 - 21:30

score 160 · Answer 9 · 2026-04-16 15:08:05

160

Views

Inverse Mellin Transform of $f(w)=\exp\big(\frac{1}{\log w}\big)?$

Published on 16 Apr 2026 - 15:08

score 278 · Answer 10 · 2026-04-10 14:38:40

278

Views

How do I find the x value of an undefined tangent function

Published on 10 Apr 2026 - 14:38

score 149 · Answer 11 · 2026-04-16 13:48:45

149

Views

How to compute $\int_{1}^{\infty} dx \sin(\beta x)e^{-\alpha x}x^n $or express it in terms of special functions?

Published on 16 Apr 2026 - 13:48

score 67 · Answer 12 · 2026-04-16 06:45:46

67

Views

How to compute $\int_{1}^{\infty} dx \sin \beta x e^{-\alpha x}x^n $or express it in terms of special functions?

Published on 16 Apr 2026 - 6:45

score 408 · Answer 13 · 2026-04-13 10:42:46

408

Views

The limit form representation of gamma function

Published on 13 Apr 2026 - 10:42

score 330 · Answer 14 · 2026-04-15 22:44:46

330

Views

Is there a closed form of the Laplace Limit Constant: $x$ such that $\frac{xe^{\sqrt{x^2+1}}}{\sqrt{x^2+1}+1}=1$ using library functions?

Published on 15 Apr 2026 - 22:44

score 112 · Answer 15 · 2026-04-16 03:48:35

112

Views

Compute $\int_{-\infty}^{+\infty}\frac{e^{i\sqrt{a^2-x^2}}}{\sqrt{a^2-x^2}}\mathrm{d}x$

Published on 16 Apr 2026 - 3:48

List Question

Is the function $f(x)=\frac{\left(1-x^2+\sqrt{\left(1-x^2\right)^2}\right)}{2}e^{-\frac{x^2}{1-x^2}}$ a bump-function $\in C_c^\infty$? Diff. Eq.?

Are these functions Absolute Continuous? (continuous nowhere-differentiable functions)

Is each of $\int_0^\infty\frac{dx}{x^x},\int_0^\infty\frac{dx}{x^{x^{x^x}}},\int_0^\infty\frac{dx}{x^{x^{x^{x^{x^x}}}}},\cdots$ less than $2$?

Expressing an exponential with a sum of mathieu functions

Asymptotic expression around $x=\infty$ of Infinite sum of the exponential integral: $\sum_{i=1,3,5..}\text{Ei}\left(\frac{-i^2 \pi^3}{4 x^2}\right)$

Proving $48\sum\limits_{n\ge1}{e^{2n}(1+e^{4n})\over(1-e^{4n})^2}=24\pi^2\sum\limits_{n\ge1}{e^{\pi^2n}(1+e^{2\pi^2n})\over(1-e^{2\pi^2n})^2}+\pi^2-2$

Asymptotics of an integral involving a Bessel function does not yield expected result

Why Dottie$=2\sqrt{I^{-1}_\frac12(\frac 12,\frac 32)-I^{-1}_\frac12(\frac 12,\frac 32)^2} = \sin^{-1}\big(1-2I^{-1}_\frac12(\frac 12,\frac 32)\big)$?

Inverse Mellin Transform of $f(w)=\exp\big(\frac{1}{\log w}\big)?$

How do I find the x value of an undefined tangent function

How to compute $\int_{1}^{\infty} dx \sin(\beta x)e^{-\alpha x}x^n $or express it in terms of special functions?

How to compute $\int_{1}^{\infty} dx \sin \beta x e^{-\alpha x}x^n $or express it in terms of special functions?

The limit form representation of gamma function

Is there a closed form of the Laplace Limit Constant: $x$ such that $\frac{xe^{\sqrt{x^2+1}}}{\sqrt{x^2+1}+1}=1$ using library functions?

Compute $\int_{-\infty}^{+\infty}\frac{e^{i\sqrt{a^2-x^2}}}{\sqrt{a^2-x^2}}\mathrm{d}x$

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