Timeline for Discrepancy in Limit calculation: Sum of limit vs limit of sum
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
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| May 2 at 16:01 | comment | added | Prem | Please also note that the fact that large t limit of T and TTransForm[T] does not match (see my answer for the definition of TTransForm), suggests that this issue is not about Limit and Plus operations not commuting. Also note that the limit of TTransForm[T] does match with the sum of limits of T. | |
| Apr 30 at 16:20 | comment | added | Prem | It is indeed true that in general, it is not valid to replace the order of limit and integrals when infinities or singularities are involved. But, it is not the case here. The function here comes from physics, where each term is very well behaved without singularities and there are finite number of terms. In fact, there are exponentially decaying functions throughout if we simplify the expression a little. Here is a plot as a function of t. github.com/prem314/projects/blob/main/mathematica/PlotOfT.pdf | |
| Apr 30 at 15:37 | history | answered | Ulrich Neumann | CC BY-SA 4.0 |