Discussion Overview
The discussion revolves around the notation used for summation of higher order partial derivatives in LaTeX, specifically whether the expression \(\sum^{n}_{k=1}\frac{\partial^{k}u}{\partial x^{k}}\) is acceptable. The scope includes technical aspects of mathematical notation and LaTeX formatting.
Discussion Character
- Technical explanation
- Debate/contested
Main Points Raised
- One participant questions the appropriateness of writing \(\sum^{n}_{k=1}\frac{\partial^{k}u}{\partial x^{k}}\), acknowledging that \(\frac{\partial^{1}u}{\partial x^{1}}\) is considered "bad" notation.
- Another participant expresses that while the notation may look unusual, they see no objection to its use in the sum.
- A third participant seeks clarification on the context in which this sum is being used.
- One participant argues that although the notation is uncommon, it is not problematic, comparing it to the notation \(x=x^{1}\).
- Another participant suggests that the sum could also be expressed as \(\sum_{k=0}^n \frac{\partial^k u}{\partial x^k}\), noting that \(\frac{\partial^0 u}{\partial x^0}= u(x)\) is understood.
Areas of Agreement / Disagreement
Participants express differing views on the acceptability of the notation, with some seeing it as unconventional but not incorrect, while others question its clarity and context. The discussion remains unresolved regarding a consensus on the notation's validity.
Contextual Notes
There are limitations regarding the assumptions about notation standards in mathematical writing and the specific contexts in which such summations might be used.