List questions from theta-functions

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Closed-form of an integral involving a Jacobi theta function, $\int\limits_0^\infty \frac{\theta_4^{n}\left(e^{-\pi x}\right)}{1+x^2} dx$

Published on 26 Apr 2016 - 22:17

235

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Prove that $\prod_{k=1}^{\infty}\left(1-e^{-\pi{k\sqrt n}}\right)=\frac{\sqrt2 g_n^2\psi(e^{-\pi\sqrt n})}{e^{\frac{\pi\sqrt n}{12}}}$

Published on 23 May 2016 - 18:25

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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 03 Jun 2016 - 19:23

125

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General Form of Theta Functions from Functional Equations

Published on 04 Jun 2016 - 2:08

586

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$E_8$ and theta functions

Published on 09 Jun 2016 - 17:01

658

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Why do the Jacobi theta functions have a natural boundary?

Published on 16 Jun 2016 - 19:34

524

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Theta series and Jacobi theta functions

Published on 28 Jun 2016 - 10:32

450

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Coefficients of powers of the theta function

Published on 10 Apr 2013 - 16:35

659

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Extension of the Jacobi triple product identity

Published on 11 Apr 2013 - 14:59

1.4k

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series involving $\log \left(\tanh\frac{\pi k}{2} \right)$

Published on 16 Apr 2013 - 2:45

1.4k

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Convergence to $0$ of Jacobi theta function

Published on 02 Jul 2013 - 17:58

1.5k

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Theta function: Absolute convergence

Published on 05 Sep 2013 - 8:05

323

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Monstrous Moonshine for $M_{24}$?

Published on 23 Nov 2013 - 3:45

1.6k

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relation between theta function and Weierstrass elliptic function

Published on 12 Dec 2013 - 14:17

245

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Expansion of Jacobi's $\theta_3(0,q)$ in q=1

Published on 17 Dec 2013 - 1:48

List Question

Closed-form of an integral involving a Jacobi theta function, $\int\limits_0^\infty \frac{\theta_4^{n}\left(e^{-\pi x}\right)}{1+x^2} dx$

Prove that $\prod_{k=1}^{\infty}\left(1-e^{-\pi{k\sqrt n}}\right)=\frac{\sqrt2 g_n^2\psi(e^{-\pi\sqrt n})}{e^{\frac{\pi\sqrt n}{12}}}$

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

General Form of Theta Functions from Functional Equations

$E_8$ and theta functions

Why do the Jacobi theta functions have a natural boundary?

Theta series and Jacobi theta functions

Coefficients of powers of the theta function

Extension of the Jacobi triple product identity

series involving $\log \left(\tanh\frac{\pi k}{2} \right)$

Convergence to $0$ of Jacobi theta function

Theta function: Absolute convergence

Monstrous Moonshine for $M_{24}$?

relation between theta function and Weierstrass elliptic function

Expansion of Jacobi's $\theta_3(0,q)$ in q=1

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