Timeline for Is the hypergeometric function ${}_1F_2(1;a,a+\frac12;-x^2)$ an elementary function? How about its positivity, monotonicity, and convexity in $x$?
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 14 at 16:15 | comment | added | qifeng618 | My first sight is correct, I never saw it before. | |
| May 14 at 13:14 | comment | added | მამუკა ჯიბლაძე | @qifeng618 It is Georgian | |
| May 14 at 9:46 | comment | added | qifeng618 | What’s the language of your full name მამუკა ჯიბლაძე? I never saw before. Arabic language? Hebrew language? I can’t imagine. | |
| May 14 at 4:02 | comment | added | მამუკა ჯიბლაძე | Yes, that way. In fact it is not necessary to @ me in this case. If a comment is under my own post, I will be notified anyway. | |
| May 13 at 22:45 | comment | added | qifeng618 | Copy and paste, not by keyboard. I tried and succeeded @მამუკა ჯიბლაძე | |
| May 13 at 15:57 | comment | added | მამუკა ჯიბლაძე | @qifeng618 Well, you can select (with mouse, for example) the area where it is typed, copy it and then paste. | |
| May 13 at 15:33 | comment | added | qifeng618 | Yes, both of these two questions are discussing the generalized hypergeometric function ${}_1F_2$. I will carefully read them again. By the way, how can I @ you? I can't input your name via my keyboard. | |
| May 13 at 13:16 | comment | added | მამუკა ჯიბლაძე | @qifeng618 Also closely related is the question mathoverflow.net/q/98684/41291 and comments, answers and links there | |
| May 11 at 18:54 | comment | added | მამუკა ჯიბლაძე | @qifeng618 Thank you. By the way, to see immediately that when $a\to\frac12$ one obtains the exponential, the following equivalent expression is more useful:$$f(t)=1+\frac{e^t}{t^{2a-1}}\left(\Gamma(2a)-\Gamma(2a,t)\right)$$ | |
| May 11 at 14:42 | comment | added | qifeng618 | I think your observations above on the function $f(t)$ is very interesting and important. | |
| May 11 at 14:33 | comment | added | qifeng618 | The doi: doi.org/10.3390/axioms13050317 will be activated very soon. Yes, I mentioned this answer in Remark 7 of the above paper. | |
| May 10 at 20:17 | comment | added | მამუკა ჯიბლაძე | Indeed your function is "like a cosine" as this $f(t)$ is "like an exponential". For example, it satisfies the differential equation $f'(t)=\frac{2a-1}t+\left(1-\frac{2a-1}t\right)f(t)$. It is interesting whether $f(t)$ satisfies some functional equation expressing $f(x+y)$ or some more complicated analog of the functional equation for the exponential function. | |
| May 10 at 19:39 | comment | added | მამუკა ჯიბლაძე | @qifeng618 Thank you for the information. DOI actually does not work, a working link that I found is https://www.mdpi.com/2075-1680/13/5/317/pdf. You mean the content of Remark 7, right? | |
| May 10 at 15:45 | comment | added | qifeng618 | Please read the paper "Yue-Wu Li and Feng Qi, A new closed-form formula of the Gauss hypergeometric function at specific arguments, Axioms 13 (2024), no. 5, Article 317, 24 pages; available online at doi.org/10.3390/axioms13050317." | |
| Nov 13, 2023 at 7:02 | history | edited | მამუკა ჯიბლაძე | CC BY-SA 4.0 |
correction
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| Nov 12, 2023 at 6:25 | history | answered | მამუკა ჯიბლაძე | CC BY-SA 4.0 |