Question

About the asymptotic behavior of specific Jacobi $\theta$ function $\operatorname{\vartheta}_3\left(0;x\right)$ when $x\to{1-}$.

score 480 · Answer 1 · 2021-09-26 07:21:24

480

Views

About the asymptotic behavior of specific Jacobi $\theta$ function $\operatorname{\vartheta}_3\left(0;x\right)$ when $x\to{1-}$.

Published on 26 Sep 2021 - 7:21

score 119 · Answer 2 · 2021-10-03 08:26:21

119

Views

Solving for $x$ the equation $\operatorname{\vartheta}_3\left(0,x\right)=k \qquad (k \geq 1)$

Published on 03 Oct 2021 - 8:26

score 186 · Answer 3 · 2026-02-23 07:23:07

186

Views

Does this Auxiliary Fresnel Sum=$\frac1{2\sqrt2\pi}\int \limits_0^\infty \frac{\vartheta_3\left(e^{-\frac{\pi x}2}\right)\sqrt x}{x^2+1}dx +\frac14 $?

Published on 23 Feb 2026 - 7:23

score 167 · Answer 4 · 2021-10-23 09:33:33

167

Views

Connection between elliptic integrals and theta functions

Published on 23 Oct 2021 - 9:33

score 113 · Answer 5 · 2021-10-25 21:48:08

113

Views

Is there an analytic expression for $\sum\limits_{n=0}^{\infty}x^{n^2}$

Published on 25 Oct 2021 - 21:48

score 76 · Answer 6 · 2021-11-04 10:23:04

76

Views

A "surprising" asymptotic inverse of $\vartheta _3(0,x)$

Published on 04 Nov 2021 - 10:23

score 50 · Answer 7 · 2021-11-17 06:10:06

50

Views

Evaluating pattern for summation of Euler-like product

Published on 17 Nov 2021 - 6:10

score 103 · Answer 8 · 2021-12-02 14:41:51

103

Views

Can I express this sum as product of two theta functions?

Published on 02 Dec 2021 - 14:41

score 155 · Answer 9 · 2021-12-04 23:57:59

155

Views

$\sum_{n=1}^{\infty} \frac{\sin(n^2)}{n^2}$

Published on 04 Dec 2021 - 23:57

score 376 · Answer 10 · 2022-01-18 21:03:17

376

Views

Relation Between Jacobi's Theta Function and Weierstrass $\wp$ Function

Published on 18 Jan 2022 - 21:03

score 183 · Answer 11 · 2022-02-19 00:21:23

183

Views

Gaussian integral using Euler/Jacobi theta function and $r_2(k)$ (number of representations as sum of 2 squares)

Published on 19 Feb 2022 - 0:21

score 216 · Answer 12 · 2022-02-24 17:06:48

216

Views

Is this function an alternative solution to the nonlinear pendulum?

Published on 24 Feb 2022 - 17:06

score 84 · Answer 13 · 2022-03-03 06:26:56

84

Views

Jacobi Elliptic function in terms of theta functions

Published on 03 Mar 2022 - 6:26

score 109 · Answer 14 · 2022-04-03 03:33:56

109

Views

Is there any definition for this series function $f(s)=\sum_{n=1}^\infty e^{-n^s}$?

Published on 03 Apr 2022 - 3:33

score 245 · Answer 15 · 2022-04-09 21:52:25

245

Views

Verifying Modularity for the Theta Function

Published on 09 Apr 2022 - 21:52

List Question

About the asymptotic behavior of specific Jacobi $\theta$ function $\operatorname{\vartheta}_3\left(0;x\right)$ when $x\to{1-}$.

Solving for $x$ the equation $\operatorname{\vartheta}_3\left(0,x\right)=k \qquad (k \geq 1)$

Does this Auxiliary Fresnel Sum=$\frac1{2\sqrt2\pi}\int \limits_0^\infty \frac{\vartheta_3\left(e^{-\frac{\pi x}2}\right)\sqrt x}{x^2+1}dx +\frac14 $?

Connection between elliptic integrals and theta functions

Is there an analytic expression for $\sum\limits_{n=0}^{\infty}x^{n^2}$

A "surprising" asymptotic inverse of $\vartheta _3(0,x)$

Evaluating pattern for summation of Euler-like product

Can I express this sum as product of two theta functions?

$\sum_{n=1}^{\infty} \frac{\sin(n^2)}{n^2}$

Relation Between Jacobi's Theta Function and Weierstrass $\wp$ Function

Gaussian integral using Euler/Jacobi theta function and $r_2(k)$ (number of representations as sum of 2 squares)

Is this function an alternative solution to the nonlinear pendulum?

Jacobi Elliptic function in terms of theta functions

Is there any definition for this series function $f(s)=\sum_{n=1}^\infty e^{-n^s}$?

Verifying Modularity for the Theta Function

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