List questions from analytic-continuation

Published on 23 Feb 2023 - 18:12

110

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Analytic continuation of $I(s)=\frac{1}{\Gamma(s)}\int^\infty_0 f(x)x^{s-1}\, dx$

Published on 26 Feb 2023 - 17:40

98

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Closed form of series $\sum_{n=\frac {1}{2}}^{\infty}\Gamma (1-s,xn)e^{xn}n^{s-1}$

Published on 02 Mar 2023 - 9:34

235

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Analytic continuation of a lambert series $f(z)=\sum_{n=1}^\infty \frac{2^n z^n}{1-(z/2)^n}$?

Published on 22 Mar 2026 - 8:56

71

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Roots and analytic continuation of $\zeta(s)=\sum_{n>0} \frac{H_n^{-s}}{n} $?

Published on 12 Mar 2023 - 20:59

80

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Analytical continuation of $\sum_{n=-\infty}^\infty \frac{\csc\left(\pi z(n+\frac{1}{2})\right)}{\Gamma\left(1+ z(n+\frac{1}{2})\right)}$

Published on 14 Mar 2023 - 0:10

142

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Help with a step on a proof of the maximum principle for harmonic functions over a connected region

Published on 23 Feb 2026 - 14:57

76

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Branch cut/ points for square roots inside cubic roots- incorrect branching by mathematica or my mistake?

Published on 25 Mar 2026 - 6:34

154

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what are the branch points and branches of $g(z)=(z+ \sqrt{z})^{1/3}$?

Published on 25 Mar 2026 - 6:34

38

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Analytic continuation of integral representation as Cauchy principal value

Published on 25 Mar 2026 - 16:12

114

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Rudin's proof of Monodromy theorem.

Published on 22 Apr 2023 - 22:26

105

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Existence of holomorphic $f$ with $(f(z))^4=z^4+4$

Published on 09 May 2023 - 11:34

156

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Regularizing infinite sum over $\sqrt{n^2+a^2}$

Published on 13 May 2023 - 23:14

191

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Analytic continuation of a series $\Psi(s)$?

Published on 19 May 2023 - 22:10

29

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Analytical continuation of $-\frac{t^w}{\ln(2)}\sum_{k=-\infty}^\infty \frac{t^{w k}}{e^{\pi i w(1+2k)}-1}$

Published on 24 May 2023 - 17:13

List Question

Analytic continuation of mandelbrot function

Analytic continuation of $I(s)=\frac{1}{\Gamma(s)}\int^\infty_0 f(x)x^{s-1}\, dx$

Closed form of series $\sum_{n=\frac {1}{2}}^{\infty}\Gamma (1-s,xn)e^{xn}n^{s-1}$

Analytic continuation of a lambert series $f(z)=\sum_{n=1}^\infty \frac{2^n z^n}{1-(z/2)^n}$?

Roots and analytic continuation of $\zeta(s)=\sum_{n>0} \frac{H_n^{-s}}{n} $?

Analytical continuation of $\sum_{n=-\infty}^\infty \frac{\csc\left(\pi z(n+\frac{1}{2})\right)}{\Gamma\left(1+ z(n+\frac{1}{2})\right)}$

Help with a step on a proof of the maximum principle for harmonic functions over a connected region

Branch cut/ points for square roots inside cubic roots- incorrect branching by mathematica or my mistake?

what are the branch points and branches of $g(z)=(z+ \sqrt{z})^{1/3}$?

Analytic continuation of integral representation as Cauchy principal value

Rudin's proof of Monodromy theorem.

Existence of holomorphic $f$ with $(f(z))^4=z^4+4$

Regularizing infinite sum over $\sqrt{n^2+a^2}$

Analytic continuation of a series $\Psi(s)$?

Analytical continuation of $-\frac{t^w}{\ln(2)}\sum_{k=-\infty}^\infty \frac{t^{w k}}{e^{\pi i w(1+2k)}-1}$

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