Timeline for Finding the roots of Hypergeometric1F1[]
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 4, 2012 at 9:34 | comment | added | acl | This is nice.${}$ | |
| Aug 3, 2012 at 22:29 | comment | added | J. M.'s missing motivation | @Sony, As I said, it's derived from the asymptotic behavior of the Kummer function. If you'll look at the formula I linked to, I took the first Bessel function term, substituted in your parameters, and then inverted that in terms of BesselJZero[]. | |
| Aug 3, 2012 at 22:25 | comment | added | Sony | I have one more question. In the code, ED[n_, β_, k_Integer:1], why did you use {λ, BesselJZero[n, k]^2 - 2 n β}? I am confused. | |
| Aug 3, 2012 at 22:21 | comment | added | Sony | Okay, Thank you! | |
| Aug 3, 2012 at 22:06 | comment | added | J. M.'s missing motivation | @Sony: Ah, so that's why the asymptotics worked particularly well here (see, you could have mentioned things like those in your question!); still, I'm wondering where you're getting 30.4715; ED[3, 10^-4] gives 40.70586582284382, and N[BesselJZero[3, 1]^2] gives 40.70646581820033. So, where did these values come from? Anyway, do check the output of Table[BesselJZero[n, 1]^2, {n, 0, 10}] // N, and you'll see that some of your values could not have come from that. | |
| Aug 3, 2012 at 22:00 | comment | added | Sony | These are the values when β approaches to 0 which are the same as the (BesselJZero[n,k])^2. For example, when n=0 & β=0.0001, we get λ=5.78306. | |
| Aug 3, 2012 at 21:50 | comment | added | J. M.'s missing motivation | @Sony, "should be" - how did you compute these values, first of all? Where did these come from? | |
| Aug 3, 2012 at 21:25 | comment | added | Sony | Can we get the plot with λ and β for each n, (n=0,...,10)? The y-intercepts should be {5.78306, 14.6819, 26.3744, 30.4715, 40.707, 49.2186, 57.5823, 70.8493, 74.8865, 76.9392, 95.2771}. | |
| Aug 3, 2012 at 4:10 | history | edited | J. M.'s missing motivation | CC BY-SA 3.0 | grammar |
| Aug 3, 2012 at 3:34 | history | answered | J. M.'s missing motivation | CC BY-SA 3.0 |