Question

Is there an analytic solution for $x^r - x + a = 0$?

score 409 · Answer 1 · 2026-04-11 16:20:17

409

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Is there an analytic solution for $x^r - x + a = 0$?

Published on 11 Apr 2026 - 16:20

score 160 · Answer 2 · 2026-04-09 07:43:17

160

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Closed form expression for continued fraction

Published on 09 Apr 2026 - 7:43

score 170 · Answer 3 · 2021-12-09 02:37:35

170

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Compute $\int_{0}^{\infty}\frac{e^{-ax-\frac{b}{x}}}{x^{3/2}}dx$

Published on 09 Dec 2021 - 2:37

score 91 · Answer 4 · 2026-04-03 20:17:09

91

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For $a>0$, what is $\int_1^\infty dy \, \exp(-ay) (y^2-1)^{-1/2}y^{-2}$?

Published on 03 Apr 2026 - 20:17

score 235 · Answer 5 · 2021-12-12 08:07:00

235

Views

Integral $\int_{0}^{\infty }\!{\frac {t\ln \left( {t}^{2}+1 \right) }{{{\rm e}^ {4\,\pi\,t}}+1}}\,{\rm d}t$

Published on 12 Dec 2021 - 8:07

score 161 · Answer 6 · 2021-12-12 18:13:04

161

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Closed expression for $\int_{-\pi}^{\pi}\sqrt{a^{2}-2ab\cos(x)+b^{2}}dx $

Published on 12 Dec 2021 - 18:13

score 65 · Answer 7 · 2026-04-11 22:13:58

65

Views

How to prove this equality with closed form?

Published on 11 Apr 2026 - 22:13

score 109 · Answer 8 · 2021-12-14 17:02:02

109

Views

Evaluate $\int_{0}^{\infty }\!{\frac {t}{{{\rm e}^{3\,\pi\,t}}-1}\ln \left( {t} ^{2}+{\frac{1}{4}} \right) }\,{\rm d}t$

Published on 14 Dec 2021 - 17:02

score 121 · Answer 9 · 2026-03-27 18:57:08

121

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Examples of closed forms of integrals with a power tower argument using W-Lambert function.

Published on 27 Mar 2026 - 18:57

score 61 · Answer 10 · 2021-12-17 15:40:48

Finding all solutions of $2\sin(c_1\omega)+\sin(c_2\omega)=0$ for $\omega$, when $c_1$ and $c_2$ are given positive real numbers?

score 112 · Answer 11 · 2021-12-19 21:06:42

112

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Solving $xy’’’+(1-m)y’’+2y=0,y=y(x)$ to prove hypergeometric representation of Abramowitz function from NIST.gov

Published on 19 Dec 2021 - 21:06

score 580 · Answer 12 · 2026-04-09 16:29:07

580

Views

An iterative logarithmic transformation of a power series

Published on 09 Apr 2026 - 16:29

score 231 · Answer 13 · 2026-04-11 23:59:59

231

Views

Proof Check: Non-existence of the inverse function in a given class of functions

Published on 11 Apr 2026 - 23:59

score 88 · Answer 14 · 2026-04-02 00:44:25

88

Views

Approximate $\sum\limits_{k=0}^{m-1}\frac{k}{m-k}$

Published on 02 Apr 2026 - 0:44

score 223 · Answer 15 · 2021-12-26 11:54:44

223

Views

Evaluate $\int_{\pi}^{\infty}\left(x^{2}-\sin\left(x\right)-1\right)^{-1}dx=?$

Published on 26 Dec 2021 - 11:54

List Question

Is there an analytic solution for $x^r - x + a = 0$?

Closed form expression for continued fraction

Compute $\int_{0}^{\infty}\frac{e^{-ax-\frac{b}{x}}}{x^{3/2}}dx$

For $a>0$, what is $\int_1^\infty dy \, \exp(-ay) (y^2-1)^{-1/2}y^{-2}$?

Integral $\int_{0}^{\infty }\!{\frac {t\ln \left( {t}^{2}+1 \right) }{{{\rm e}^ {4\,\pi\,t}}+1}}\,{\rm d}t$

Closed expression for $\int_{-\pi}^{\pi}\sqrt{a^{2}-2ab\cos(x)+b^{2}}dx $

How to prove this equality with closed form?

Evaluate $\int_{0}^{\infty }\!{\frac {t}{{{\rm e}^{3\,\pi\,t}}-1}\ln \left( {t} ^{2}+{\frac{1}{4}} \right) }\,{\rm d}t$

Examples of closed forms of integrals with a power tower argument using W-Lambert function.

Finding all solutions of $2\sin(c_1\omega)+\sin(c_2\omega)=0$ for $\omega$, when $c_1$ and $c_2$ are given positive real numbers?

Solving $xy’’’+(1-m)y’’+2y=0,y=y(x)$ to prove hypergeometric representation of Abramowitz function from NIST.gov

An iterative logarithmic transformation of a power series

Proof Check: Non-existence of the inverse function in a given class of functions

Approximate $\sum\limits_{k=0}^{m-1}\frac{k}{m-k}$

Evaluate $\int_{\pi}^{\infty}\left(x^{2}-\sin\left(x\right)-1\right)^{-1}dx=?$

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