Timeline for Definite integral of Gaussian divided by hyperbolic cosine
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 13 at 15:04 | answer | added | Sergio A. Yuhjtman | timeline score: 0 | |
| May 13 at 14:18 | vote | accept | Sergio A. Yuhjtman | ||
| May 4 at 10:40 | comment | added | Carlo Beenakker | I have added a source (the Hardy-Ramanujan correspondence) and the proof (it's simple) in the answer box. | |
| May 4 at 7:05 | answer | added | Carlo Beenakker | timeline score: 4 | |
| May 4 at 0:02 | comment | added | Sergio A. Yuhjtman | Thanks, Iosif and Carlo. @CarloBeenakker do you have a reference for this identity? | |
| May 2 at 21:26 | history | edited | Michael Hardy | CC BY-SA 4.0 |
added 12 characters in body
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| May 2 at 20:04 | comment | added | Carlo Beenakker | this integral was studied by Ramanujan, he could not evaluate it in closed form, however, he did derive the identity $$\sqrt{\alpha} \int_{0}^{\infty} \frac{e^{-x^2}}{\cosh\alpha x} dx=\sqrt{\beta} \int_{0}^{\infty} \frac{e^{-x^2}}{\cosh\beta x} dx$$ for $\alpha\beta=\pi$ | |
| May 2 at 17:13 | comment | added | Iosif Pinelis | Mathematica cannot do anything with this integral. So, it is unlikely to have a nice expression. | |
| May 2 at 15:52 | history | asked | Sergio A. Yuhjtman | CC BY-SA 4.0 |