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Which one of the following sentences sounds better to a native ear?

  1. At $x=a$, $f(x,t)$ is an even function of $t$.
  2. For $x=a$, $f(x,t)$ is an even function of $t$.
  3. When $x=a$, $f(x,t)$ is an even function of $t$.
  4. If $x=a$, (then) $f(x,t)$ is an even function of $t$.
  5. With $x=a$, $f(x,t)$ is an even function of $t$.
  6. Given (that) $x=a$, $f(x,t)$ is an even function of $t$.
  7. Provided (that) $x=a$, $f(x,t)$ is an even function of $t$.
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    I’m voting to close this question because this would be a better fit on a Mathematics or English SE site. Feb 2 at 14:18
  • This seems to be a question about the basic conventions of writing within your research field. You should have the idea of what the standard is from all the papers you've read so far. If still unsure how to chose between the standards, talk to your advisor.
    – penelope
    Feb 2 at 14:58
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    If a value for a has already been specified, I'd probably write "f(a,t) is an even function of t." Feb 3 at 0:37

2 Answers 2

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Focusing on “native ear”; 6. Given (that) $x=a$, $f(x,t)$ is an even function of $t$. sounds the best to me.

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There is no standard for such things, and some variety it phrasing makes reading more pleasant generally, especially in essays. The only one I haven't seen used (frequently) is the first, but that might depend on context. If your writing is too formulaic it becomes stilted and pedantic, so a good choice is one you haven't used just now. All are basically alternate phrasings of 4, which would be a symbolic-logic like formulation. In extremely formal writing 4 might be preferred.

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