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feat(analysis/complex/exponential): limits of exp #1744

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merged 10 commits into from
Nov 30, 2019

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This PR proves the following lemma

/-- The function `x^n * exp(-x)` tends to `0` at +infinity, for any natural number `n`. -/
lemma tendsto_pow_mul_exp_neg_at_top_nhds_0 (n : ℕ) : tendsto (λx, x^n * exp (-x)) at_top (𝓝 0)

along with supporting material on the exponential, functions tending to +infinity, and some linting.

@sgouezel sgouezel added the awaiting-review The author would like community review of the PR label Nov 26, 2019
@robertylewis robertylewis added ready-to-merge All that is left is for bors to build and merge this PR. (Remember you need to say `bors r+`.) and removed awaiting-review The author would like community review of the PR labels Nov 30, 2019
@mergify mergify bot merged commit 343c54d into leanprover-community:master Nov 30, 2019
@sgouezel sgouezel deleted the exp_limit branch December 2, 2019 10:37
anrddh pushed a commit to anrddh/mathlib that referenced this pull request May 15, 2020
…ty#1744)

* staging

* exp div pow

* cleanup

* oops

* better proof

* cleanup

* docstring

* typo in docstring
anrddh pushed a commit to anrddh/mathlib that referenced this pull request May 16, 2020
…ty#1744)

* staging

* exp div pow

* cleanup

* oops

* better proof

* cleanup

* docstring

* typo in docstring
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4 participants