Question

Identity of modified Bessel functions

score 131 · Answer 1 · 2020-10-04 04:03:03

131

Views

Identity of modified Bessel functions

Published on 04 Oct 2020 - 4:03

score 147 · Answer 2 · 2020-10-06 12:55:04

147

Views

How to prove this equality of series

Published on 06 Oct 2020 - 12:55

score 145 · Answer 3 · 2020-11-20 05:53:35

145

Views

Find an explicit formula for $ \sum_{n=0}^{\infty}{x^{n^2}} ,\quad \forall x \in (0,1) $

Published on 20 Nov 2020 - 5:53

score 154 · Answer 4 · 2026-03-25 11:33:43

154

Views

Has there been any exploration on Cubic Power Series?

Published on 25 Mar 2026 - 11:33

score 219 · Answer 5 · 2020-12-07 19:27:05

219

Views

Interpretation of a certain general theorem used by Gauss in his work on theta functions.

Published on 07 Dec 2020 - 19:27

score 239 · Answer 6 · 2020-12-15 13:41:36

239

Views

Equivalency between a "mixed modular equation" of Gauss and a later theorem of Ramanujan.

Published on 15 Dec 2020 - 13:41

score 64 · Answer 7 · 2020-12-19 22:56:40

64

Views

Finding $\alpha$ such that $\alpha(f(x)-\sqrt{\pi})=\cos(2\pi x)$, where $f(x)=\sum_{n\in\mathbb{Z}}{e^{-(x-n)^2}}$

Published on 19 Dec 2020 - 22:56

score 120 · Answer 8 · 2026-03-25 14:32:35

120

Views

Symbolic calculation vs. desmos

Published on 25 Mar 2026 - 14:32

score 262 · Answer 9 · 2026-02-23 05:12:25

262

Views

Square of Jacobi theta function is sum of hyperbolic secant?

Published on 23 Feb 2026 - 5:12

score 187 · Answer 10 · 2021-02-02 11:14:23

187

Views

Prove that $\sum _{n=-\infty }^{\infty } e^{-n^2 \pi x}=\frac{1}{\sqrt{x}}\sum _{n=-\infty }^{\infty } e^{-\frac{n^2 \pi }{x}}$

Published on 02 Feb 2021 - 11:14

score 307 · Answer 11 · 2021-02-15 21:58:08

307

Views

What is the connection between different definitions for theta functions?

Published on 15 Feb 2021 - 21:58

score 99 · Answer 12 · 2021-02-20 12:31:14

99

Views

What does $\sum_{n=0}^\infty z^{n(n+1)/2}$, $|z|<1$ converge to?

Published on 20 Feb 2021 - 12:31

score 44 · Answer 13 · 2021-03-15 05:20:30

44

Views

What is the coefficient of $q^n$ in the Lambert Series Expansion $a^2(q).a(q^5)$

Published on 15 Mar 2021 - 5:20

score 185 · Answer 14 · 2021-03-22 14:43:40

185

Views

Validity of $\ln z=\frac{\pi}{\operatorname{AGP}(\theta_2^2(1/z),\theta_3^2(1/z))}$

Published on 22 Mar 2021 - 14:43

score 55 · Answer 15 · 2021-04-01 19:10:32

55

Views

Proving $\vartheta'_1 (0) = \vartheta_2 (0) \vartheta_3 (0) \vartheta_4 (0)$ different from Whittaker and Watson

Published on 01 Apr 2021 - 19:10

List Question

Identity of modified Bessel functions

How to prove this equality of series

Find an explicit formula for $ \sum_{n=0}^{\infty}{x^{n^2}} ,\quad \forall x \in (0,1) $

Has there been any exploration on Cubic Power Series?

Interpretation of a certain general theorem used by Gauss in his work on theta functions.

Equivalency between a "mixed modular equation" of Gauss and a later theorem of Ramanujan.

Finding $\alpha$ such that $\alpha(f(x)-\sqrt{\pi})=\cos(2\pi x)$, where $f(x)=\sum_{n\in\mathbb{Z}}{e^{-(x-n)^2}}$

Symbolic calculation vs. desmos

Square of Jacobi theta function is sum of hyperbolic secant?

Prove that $\sum _{n=-\infty }^{\infty } e^{-n^2 \pi x}=\frac{1}{\sqrt{x}}\sum _{n=-\infty }^{\infty } e^{-\frac{n^2 \pi }{x}}$

What is the connection between different definitions for theta functions?

What does $\sum_{n=0}^\infty z^{n(n+1)/2}$, $|z|<1$ converge to?

What is the coefficient of $q^n$ in the Lambert Series Expansion $a^2(q).a(q^5)$

Validity of $\ln z=\frac{\pi}{\operatorname{AGP}(\theta_2^2(1/z),\theta_3^2(1/z))}$

Proving $\vartheta'_1 (0) = \vartheta_2 (0) \vartheta_3 (0) \vartheta_4 (0)$ different from Whittaker and Watson

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