Timeline for Series approximation to integral
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 28, 2015 at 21:02 | comment | added | Dr. Wolfgang Hintze | @bbgodfrey Thank you for the hint which led me to consider other functions than powers successfully. See my edit of today. | |
| Feb 28, 2015 at 19:04 | history | edited | Dr. Wolfgang Hintze | CC BY-SA 3.0 | Expamples of s-expansions for two functions other than powrs |
| Feb 28, 2015 at 18:59 | history | edited | Dr. Wolfgang Hintze | CC BY-SA 3.0 | Expamples of s-expansions for two functions other than powrs |
| Feb 28, 2015 at 10:22 | history | edited | Dr. Wolfgang Hintze | CC BY-SA 3.0 | Write down general expansion, and observe that it holds for more general functions. |
| Feb 26, 2015 at 21:03 | comment | added | Dr. Wolfgang Hintze | @bbgodfrey I agree completely. I tried e.g. two poles f[y] = 1/(1+y^2), without success. The y-integral must be split into one over (0..1) and the other over (1,oo). But the resulting integrals had no closed expressions. | |
| Feb 26, 2015 at 17:34 | comment | added | bbgodfrey | Although this is an elegant solution, it may be valid only if f is an entire function, so that its series converges throughout the range of integration. If not, then some additional terms associated with the poles of f in the complex plane may arise. | |
| S Feb 26, 2015 at 17:25 | history | suggested | Till Hoffmann | CC BY-SA 3.0 | added conversion of series representation to normal formula |
| Feb 26, 2015 at 17:19 | vote | accept | Till Hoffmann | ||
| Feb 26, 2015 at 17:19 | comment | added | Till Hoffmann | Dr. Wolfgang Hintze, thank you very much for your help. I would like to mention you in the acknowledgements of the paper for which I required the above series expansion. Please drop me a line at t.hoffmann13(AT)imperial(DOT)ac(DOT)uk and I will send you a draft before publication. | |
| Feb 26, 2015 at 17:14 | review | Suggested edits | |||
| S Feb 26, 2015 at 17:25 | |||||
| Feb 26, 2015 at 13:58 | comment | added | Till Hoffmann | Hi, thanks for the suggestion. Using the expansion $\mathtt{sg1}=x^k + \sigma^2 \frac{k(1+k)}{2} x^{k-1}$, the first term reproduces the desired function $f(x)$ in a Taylor expansion. How can I express the second term in terms of the original function and its derivatives? It almost looks like a second derivative. I'll have a play with it. | |
| Feb 26, 2015 at 12:42 | history | answered | Dr. Wolfgang Hintze | CC BY-SA 3.0 |