Question

An identity involving integrals of the form $\int_{0}^{\alpha} \arctan (\sqrt{5}\tan\theta) \, d\theta$.

score 703 · Answer 1 · 2013-12-02 01:25:40

703

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An identity involving integrals of the form $\int_{0}^{\alpha} \arctan (\sqrt{5}\tan\theta) \, d\theta$.

Published on 02 Dec 2013 - 1:25

score 362 · Answer 2 · 2026-04-12 06:33:21

362

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parabolic cylinder function with negative argument

Published on 12 Apr 2026 - 6:33

score 648 · Answer 3 · 2026-04-12 00:20:54

648

Views

Norm of a matrix exponential

Published on 12 Apr 2026 - 0:20

score 527 · Answer 4 · 2013-12-04 18:58:58

527

Views

Lipschitz bump function

Published on 04 Dec 2013 - 18:58

score 131 · Answer 5 · 2026-04-09 14:50:10

131

Views

How to evaluate the integral involving two Bessel functions and following elementary function?

Published on 09 Apr 2026 - 14:50

score 928 · Answer 6 · 2013-12-06 18:16:28

928

Views

Evaluate the Bessel Function $J = \int^{2\pi}_{0}{e^{\cos x}}{\cos(2x - \sin x)}\, dx$

Published on 06 Dec 2013 - 18:16

score 396 · Answer 7 · 2013-12-06 20:49:23

396

Views

Asymptotic expansion of $J(t) = \int^{\infty}_{0}{\exp(-t(x + 4/(x+1)))}\, dx$

Published on 06 Dec 2013 - 20:49

score 612 · Answer 8 · 2026-04-09 11:31:45

612

Views

The multiplication formula for the Hurwitz zeta function

Published on 09 Apr 2026 - 11:31

score 436 · Answer 9 · 2013-12-10 09:39:48

436

Views

How prove this limit $\lim_{\alpha\to n}\frac{J_{\alpha}(x)\cos{(\alpha \pi)}-J_{-\alpha}(x)}{\sin{\alpha\pi}}$?

Published on 10 Dec 2013 - 9:39

score 76 · Answer 10 · 2013-12-11 04:22:08

76

Views

How prove this $f(x,y)=\frac{1}{2\pi}\ln{\frac{1}{|x-y|}}+\frac{i}{4}-\frac{1}{2\pi}\ln{\frac{k}{2}}-\frac{C}{2\pi}$?

Published on 11 Dec 2013 - 4:22

score 216 · Answer 11 · 2013-12-12 17:35:49

216

Views

Why does $\lim_{x \rightarrow 0} B(x,y)$ exist and how is it calculated?

Published on 12 Dec 2013 - 17:35

score 7.4k · Answer 12 · 2026-04-09 19:21:04

7.4k

Views

Gamma function has no zeros

Published on 09 Apr 2026 - 19:21

score 63 · Answer 13 · 2013-12-16 01:40:38

63

Views

Show that these identities are true.

Published on 16 Dec 2013 - 1:40

score 118 · Answer 14 · 2026-04-12 17:57:01

118

Views

Choosing an appropriate complete orthogonal basis

Published on 12 Apr 2026 - 17:57

score 1.5k · Answer 15 · 2026-04-11 16:03:52

1.5k

Views

Other interesting consequences of $d=163$?

Published on 11 Apr 2026 - 16:03

List Question

An identity involving integrals of the form $\int_{0}^{\alpha} \arctan (\sqrt{5}\tan\theta) \, d\theta$.

parabolic cylinder function with negative argument

Norm of a matrix exponential

Lipschitz bump function

How to evaluate the integral involving two Bessel functions and following elementary function?

Evaluate the Bessel Function $J = \int^{2\pi}_{0}{e^{\cos x}}{\cos(2x - \sin x)}\, dx$

Asymptotic expansion of $J(t) = \int^{\infty}_{0}{\exp(-t(x + 4/(x+1)))}\, dx$

The multiplication formula for the Hurwitz zeta function

How prove this limit $\lim_{\alpha\to n}\frac{J_{\alpha}(x)\cos{(\alpha \pi)}-J_{-\alpha}(x)}{\sin{\alpha\pi}}$?

How prove this $f(x,y)=\frac{1}{2\pi}\ln{\frac{1}{|x-y|}}+\frac{i}{4}-\frac{1}{2\pi}\ln{\frac{k}{2}}-\frac{C}{2\pi}$?

Why does $\lim_{x \rightarrow 0} B(x,y)$ exist and how is it calculated?

Gamma function has no zeros

Show that these identities are true.

Choosing an appropriate complete orthogonal basis

Other interesting consequences of $d=163$?

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