List questions from divergent-integrals

Published on 01 Dec 2020 - 4:47

195

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Are there any good examples from other math fields or intuition supporting $\int_0^1\frac1xdx=\int_1^\infty\frac1xdx$?

Published on 24 Dec 2020 - 1:29

72

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Can one represent divergent integrals or germs at infinity with surreal numbers?

Published on 01 Jan 2021 - 17:34

240

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Interpreting the logarithm as a sum of simple poles along the negative real axis

Published on 10 Jan 2021 - 9:10

436

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Prove that Gamma function is divergent for $\Re(z)\leq 0$

Published on 27 Jan 2021 - 8:28

114

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Integral representation of $f(x)=0^x$

Published on 21 Mar 2021 - 0:34

274

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Why is $\ln 0\ne-\ln \infty$?

Published on 25 Mar 2021 - 10:18

54

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Can we assign meaningful values to $\int_{-a}^bf(x)/x^n\,\mathrm dx$ for $n=2,3,\dots$

Published on 30 Mar 2021 - 13:48

560

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Fourier transforms: divergent integrals?

Published on 31 Mar 2021 - 17:15

286

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Contour integral $\int_{C_\varepsilon}\frac{e^{i\alpha\omega}}{\omega^2}\mathrm{d}\omega$

Published on 22 May 2021 - 15:45

126

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Does the Euler-Mascheroni constant $\gamma$ correspond to infinite hyperbolic angle?

Published on 28 May 2021 - 11:39

126

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Do these constants appear in other areas of mathematics?

Published on 29 May 2021 - 0:34

144

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Divergent integral using contour

Published on 23 Jul 2021 - 17:09

87

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inequivalence of Fourier transform?

Published on 28 Sep 2021 - 16:43

169

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Why does the integral $\int_{1}^{\infty} x^p \,dx$ diverge for values of $p ≤ 1$?

Published on 05 Oct 2021 - 15:53

List Question

How to determine that the improper integral $\int_{\pi}^{\infty}\frac{\sin^2(x)}{x}dx$ diverges?

Are there any good examples from other math fields or intuition supporting $\int_0^1\frac1xdx=\int_1^\infty\frac1xdx$?

Can one represent divergent integrals or germs at infinity with surreal numbers?

Interpreting the logarithm as a sum of simple poles along the negative real axis

Prove that Gamma function is divergent for $\Re(z)\leq 0$

Integral representation of $f(x)=0^x$

Why is $\ln 0\ne-\ln \infty$?

Can we assign meaningful values to $\int_{-a}^bf(x)/x^n\,\mathrm dx$ for $n=2,3,\dots$

Fourier transforms: divergent integrals?

Contour integral $\int_{C_\varepsilon}\frac{e^{i\alpha\omega}}{\omega^2}\mathrm{d}\omega$

Does the Euler-Mascheroni constant $\gamma$ correspond to infinite hyperbolic angle?

Do these constants appear in other areas of mathematics?

Divergent integral using contour

inequivalence of Fourier transform?

Why does the integral $\int_{1}^{\infty} x^p \,dx$ diverge for values of $p ≤ 1$?

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