Timeline for Computing $_2F_2(a,a,a+1,a+1,z)$ (hypergeometric function)
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Jan 24 at 12:06 | comment | added | Claude Leibovici | Did you look at Kummer-type transformations ? | |
| Jan 20, 2023 at 19:36 | answer | added | Alexandru Ionut | timeline score: 0 | |
| Jan 20, 2023 at 19:02 | answer | added | Aaron Hendrickson | timeline score: 1 | |
| Jan 20, 2023 at 7:54 | comment | added | lrnv |
@RobertIsrael Thanks, wolfram reduced this for integers a too, but I am interested in general a. @AaronHendrickson, Yes, I am looking for a good way to evaluate it correctly !
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| Jan 19, 2023 at 22:30 | answer | added | Fred Hucht | timeline score: 2 | |
| Jan 19, 2023 at 20:24 | comment | added | Aaron Hendrickson | Are you just looking for ways to numerically evaluate this hypergeometric function? | |
| Jan 19, 2023 at 18:09 | comment | added | Robert Israel | And for $a=2$, $$ 4 \frac{e^z - \text{Ei}(z) +\gamma-1+\ln(z)}{z^2} $$ | |
| Jan 19, 2023 at 17:52 | comment | added | Robert Israel | If $a$ is a positive integer, it seems you can express it in terms of exponential integral or incomplete Gamma functions. Thus for $a=1$, it is $$\frac{\,\mathrm{Ei}\! \left(z \right)- \gamma -\ln \! \left(z \right)}{ z}$$ | |
| Jan 19, 2023 at 17:15 | comment | added | Gerald Edgar | This series satisfies the differential equation $$F \left( z \right) {a}^{2}+ \left( 2\,a+1 \right)z {\frac {\rm d}{ {\rm d}z}}F \left( z \right) +{z}^{2}{\frac {{\rm d}^{2}}{{\rm d}{z}^{ 2}}}F \left( z \right) ={a}^{2}{{\rm e}^{z}}$$But when I ask Maple to solve this DE, I get something involving that ${}_2F_2$. | |
| Jan 19, 2023 at 16:56 | comment | added | Carlo Beenakker | it does not reduce to any elementary function. | |
| Jan 19, 2023 at 16:29 | history | asked | lrnv | CC BY-SA 4.0 |