Question

proving sigma = BigTheta (BigΘ)

score 112 · Answer 1 · 2026-03-22 11:18:54

112

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proving sigma = BigTheta (BigΘ)

Published on 22 Mar 2026 - 11:18

score 172 · Answer 2 · 2026-03-17 08:54:06

172

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The even-index reciprocal Lucas constant and $\sum_{n=1}^\infty \frac1{x_1^{2n}+x_2^{2n}}$

Published on 17 Mar 2026 - 8:54

score 572 · Answer 3 · 2026-03-19 14:06:17

572

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Asymptotic equivalent of $\sum_{n\ge0} q^{n^2}{x^n}$ as $x\to+\infty$

Published on 19 Mar 2026 - 14:06

score 89 · Answer 4 · 2026-03-22 06:49:52

89

Views

Basic $\theta$-function identity proof

Published on 22 Mar 2026 - 6:49

score 191 · Answer 5 · 2026-03-22 06:41:43

191

Views

How to show that the theta function is smooth?

Published on 22 Mar 2026 - 6:41

score 77 · Answer 6 · 2026-03-20 02:54:28

77

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$\theta(z) = \sum_{n=-\infty}^{+\infty} e^{\frac{-n^2}{2}}e^{inz}$ How to show $\theta '(\frac{i}{2}) = \frac{-i}{2} \theta (\frac{i}{2})$?

Published on 20 Mar 2026 - 2:54

score 288 · Answer 7 · 2026-03-20 12:48:12

288

Views

$\Theta$ function in terms of Weierstraß $\sigma$ function?

Published on 20 Mar 2026 - 12:48

score 142 · Answer 8 · 2026-03-19 19:02:04

142

Views

Properties of $\frac {\theta_{1}''(z|\tau)}{\theta_{1}(z|\tau)}$?

Published on 19 Mar 2026 - 19:02

score 89 · Answer 9 · 2026-03-20 10:59:18

89

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$\sum\limits_{\mathbb{d|n}}{f(d)}=\sum\limits_{\mathbb{d|n}}{g(d)}\implies f(n)=g(n)?$

Published on 20 Mar 2026 - 10:59

score 236 · Answer 10 · 2026-03-22 12:26:49

236

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How many integer solutions are there on an $n$ dimensional hypersphere of radius $\sqrt{r}$ centered at the origin?

Published on 22 Mar 2026 - 12:26

score 178 · Answer 11 · 2026-03-22 08:47:02

178

Views

Clarification of Landau's Mechanics, Chapter.6 & Whittaker, Analytical Dynamics Chapter.6 needed

Published on 22 Mar 2026 - 8:47

score 312 · Answer 12 · 2026-03-22 11:04:21

312

Views

How many integer pairs satisfy the ellipse $x^2+ay^2=r?$

Published on 22 Mar 2026 - 11:04

score 247 · Answer 13 · 2026-03-22 05:46:28

247

Views

What's the connection between $\theta$ series and the number of integer solutions on a curve? Proof Verification

Published on 22 Mar 2026 - 5:46

score 821 · Answer 14 · 2026-03-22 09:54:00

821

Views

How are the Jacobi Theta Functions analogous to the Exponential Function?

Published on 22 Mar 2026 - 9:54

score 107 · Answer 15 · 2026-03-21 17:45:15

107

Views

Analytic continuation of Riemann Theta function to positive semidefinite matrices

Published on 21 Mar 2026 - 17:45

List Question

proving sigma = BigTheta (BigΘ)

The even-index reciprocal Lucas constant and $\sum_{n=1}^\infty \frac1{x_1^{2n}+x_2^{2n}}$

Asymptotic equivalent of $\sum_{n\ge0} q^{n^2}{x^n}$ as $x\to+\infty$

Basic $\theta$-function identity proof

How to show that the theta function is smooth?

$\theta(z) = \sum_{n=-\infty}^{+\infty} e^{\frac{-n^2}{2}}e^{inz}$ How to show $\theta '(\frac{i}{2}) = \frac{-i}{2} \theta (\frac{i}{2})$?

$\Theta$ function in terms of Weierstraß $\sigma$ function?

Properties of $\frac {\theta_{1}''(z|\tau)}{\theta_{1}(z|\tau)}$?

$\sum\limits_{\mathbb{d|n}}{f(d)}=\sum\limits_{\mathbb{d|n}}{g(d)}\implies f(n)=g(n)?$

How many integer solutions are there on an $n$ dimensional hypersphere of radius $\sqrt{r}$ centered at the origin?

Clarification of Landau's Mechanics, Chapter.6 & Whittaker, Analytical Dynamics Chapter.6 needed

How many integer pairs satisfy the ellipse $x^2+ay^2=r?$

What's the connection between $\theta$ series and the number of integer solutions on a curve? Proof Verification

How are the Jacobi Theta Functions analogous to the Exponential Function?

Analytic continuation of Riemann Theta function to positive semidefinite matrices

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