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Results tagged with closed-form-expressions
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user 489481
For questions that specifically ask for determining a closed form of equations, integrals etc.
2
votes
0
answers
106
views
Ratio of theta function derivatives with theta function
I have the following ratios I want to compute.
$$ \frac{ \left( \frac{\partial \vartheta_3(v, q)}{\partial v} \right)^2 }{C + \left(\vartheta_3(v, q)\right)^2 }, $$
where $C$ is a constant.
$$ \frac{ …
- 159
2
votes
1
answer
177
views
Is this integral solvable analytically?
I have this integral that comes from my research with some Fourier Transforms of spectrum functions:
$$ G(\tau) = \int_{0}^{\infty} e^{-\Lambda x} x^n e^{i \tau ( c_1 - c_2 e^{-c_3 x} ) } dx $$
where …
- 188k
0
votes
0
answers
74
views
How to perform this integral to get a closed/ semi closed form
I want to get a closed/ semi-closed form of the integral given below.
$$ \int_{-\infty}^{+\infty} \exp{\left(-\frac{(x - \mu)^2}{2\sigma^2}\right)} \text{erf}\left(\alpha \frac{x-\mu}{\sqrt{2}\sigma}\ …
- 159