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Family of definite integrals involving Dedekind eta function of a complex argument, $\int_0^{\infty} \eta^k(ix)dx$

score 1.9k · Answer 1 · 2026-03-26 08:00:32

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Family of definite integrals involving Dedekind eta function of a complex argument, $\int_0^{\infty} \eta^k(ix)dx$

Published on 26 Mar 2026 - 8:00

score 1k · Answer 2 · 2026-04-06 11:34:38

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Integral of incomplete gamma function and limit of hypergeometric function

Published on 06 Apr 2026 - 11:34

score 374 · Answer 3 · 2016-06-04 10:00:39

374

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Integral representation of a Meijer G-function

Published on 04 Jun 2016 - 10:00

score 106 · Answer 4 · 2016-06-06 11:10:57

106

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The function $\zeta(\frac{1}{2}+it) \left[ \sqrt{2}\left( \cos(t\log 2)+i\sin(t\log 2) \right) -2 \right]$ has a numerical root

Published on 06 Jun 2016 - 11:10

score 2.8k · Answer 5 · 2026-03-27 03:43:21

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How to express $2x^3-x^2-3x+2$ as a linear combination of Legendre polynomials

Published on 27 Mar 2026 - 3:43

score 123 · Answer 6 · 2016-06-08 08:07:27

123

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Unconventional Differentiation Rules

Published on 08 Jun 2016 - 8:07

score 1.2k · Answer 7 · 2026-03-25 17:38:24

1.2k

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Limit of gamma and digamma function

Published on 25 Mar 2026 - 17:38

score 552 · Answer 8 · 2016-06-09 08:48:30

552

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Series expansion of $\int x^xdx$

Published on 09 Jun 2016 - 8:48

score 165 · Answer 9 · 2026-04-06 21:30:27

165

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Integration of Laguerre polynomial $\int_{0}^{x}u^{p-1}(1-u)^{q-1}e^{-\theta u}L_n^{(m)}(\theta u)\mathrm du$

Published on 06 Apr 2026 - 21:30

score 229 · Answer 10 · 2016-06-10 16:19:18

229

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Proof of a formula containing double factorial

Published on 10 Jun 2016 - 16:19

score 302 · Answer 11 · 2026-04-01 20:25:43

302

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Verify $y=x^{1/2}Z_{1/3}\left(2x^{3/2}\right)$ is a solution to $y^{\prime\prime}+9xy=0$

Published on 01 Apr 2026 - 20:25

score 741 · Answer 12 · 2026-04-01 20:25:42

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Prove $\int_0^{\pi/2} J_0 (\cos x) dx=\frac{\pi}{2} \left(J_0 \left(\frac{1}{2} \right)\right)^2$

Published on 01 Apr 2026 - 20:25

score 1.7k · Answer 13 · 2026-02-24 03:41:32

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Deriving the Airy functions from first principles

Published on 24 Feb 2026 - 3:41

score 82 · Answer 14 · 2026-03-26 18:40:53

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Proof of $\Gamma(x)\Gamma\left(\dfrac{1}{x}\right)\gt 1$

Published on 26 Mar 2026 - 18:40

score 1.3k · Answer 15 · 2016-06-14 14:01:27

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Integration of physicists' Hermite polynomial with exponential

Published on 14 Jun 2016 - 14:01

List Question

Family of definite integrals involving Dedekind eta function of a complex argument, $\int_0^{\infty} \eta^k(ix)dx$

Integral of incomplete gamma function and limit of hypergeometric function

Integral representation of a Meijer G-function

The function $\zeta(\frac{1}{2}+it) \left[ \sqrt{2}\left( \cos(t\log 2)+i\sin(t\log 2) \right) -2 \right]$ has a numerical root

How to express $2x^3-x^2-3x+2$ as a linear combination of Legendre polynomials

Unconventional Differentiation Rules

Limit of gamma and digamma function

Series expansion of $\int x^xdx$

Integration of Laguerre polynomial $\int_{0}^{x}u^{p-1}(1-u)^{q-1}e^{-\theta u}L_n^{(m)}(\theta u)\mathrm du$

Proof of a formula containing double factorial

Verify $y=x^{1/2}Z_{1/3}\left(2x^{3/2}\right)$ is a solution to $y^{\prime\prime}+9xy=0$

Prove $\int_0^{\pi/2} J_0 (\cos x) dx=\frac{\pi}{2} \left(J_0 \left(\frac{1}{2} \right)\right)^2$

Deriving the Airy functions from first principles

Proof of $\Gamma(x)\Gamma\left(\dfrac{1}{x}\right)\gt 1$

Integration of physicists' Hermite polynomial with exponential

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