Timeline for Analytical approximation of indefinite integral on a given interval to a given precision
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 3, 2016 at 19:22 | answer | added | Michael E2 | timeline score: 9 | |
| Aug 2, 2016 at 16:53 | comment | added | Michael | @bbgodfrey: by analytical approximation I meant a closed form solution in term of elementary functions and other NPU-supported special functions ($erf, gamma$, etc) of $a,b,c$. Basically I want to plug $a,b,c$ into the analytical expression and get the above integral with accuracy $\epsilon$. | |
| Aug 2, 2016 at 16:47 | vote | accept | Michael | ||
| Aug 2, 2016 at 11:59 | history | edited | J. M.'s missing motivation | CC BY-SA 3.0 | added 12 characters in body |
| Aug 2, 2016 at 11:26 | answer | added | Mariusz Iwaniuk | timeline score: 6 | |
| Aug 2, 2016 at 4:14 | comment | added | J. M.'s missing motivation | I don't agree with the proposed duplicate. OP's function has qualitatively different properties from the function in the other thread. Note that in this case both factors tend to a limit with increasing $b\gg c$, while the function in the other thread has an $\exp(x^2)$ factor whose blow-up is only mitigated by the complementary error function. | |
| Aug 2, 2016 at 3:54 | comment | added | bbgodfrey | Note that an analytical solution does exist for c == 0, 1/4 Sqrt[π] (-Erf[a]^2 + Erf[b]^2). | |
| Aug 2, 2016 at 1:12 | comment | added | bbgodfrey | What is your definition of analytical approximation? InterpolationFunction is an analytical approximation in the sense that it fits arrays of numbers to splines or Hermite polynomials, but I suspect that it is not what you are seeking. | |
| Aug 2, 2016 at 0:25 | review | Close votes | |||
| Aug 2, 2016 at 4:15 | |||||
| Aug 2, 2016 at 0:06 | comment | added | Artes | Possible duplicate of Numerical underflow for a scaled error function | |
| Aug 1, 2016 at 23:49 | comment | added | Michael | @J.M.: $-5<a,b,c<5$ would be good. | |
| Aug 1, 2016 at 23:44 | comment | added | J. M.'s missing motivation | "within a certain range" - can you please specify those ranges for completeness? | |
| Aug 1, 2016 at 23:44 | history | edited | J. M.'s missing motivation | edited tags; edited tags | |
| Aug 1, 2016 at 23:37 | history | asked | Michael | CC BY-SA 3.0 |