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[Merged by Bors] - feat(special_functions/gamma): Bohr-Mollerup theorem #18188

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Add the characterisation of the Gamma function as the unique log-convex function with the correct functional equation.


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@loefflerd loefflerd marked this pull request as ready for review January 16, 2023 12:56
@loefflerd loefflerd added the awaiting-review The author would like community review of the PR label Jan 17, 2023
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@sgouezel sgouezel added awaiting-author A reviewer has asked the author a question or requested changes and removed awaiting-review The author would like community review of the PR labels Jan 17, 2023
loefflerd and others added 4 commits January 17, 2023 21:56
@loefflerd loefflerd added awaiting-review The author would like community review of the PR and removed awaiting-author A reviewer has asked the author a question or requested changes labels Jan 18, 2023
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Thanks for the review! I've updated it as you suggested. (I've also relabelled the variables in the main convexity proof to avoid the slightly disturbing concept of L_(1/p)-space.)

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@sgouezel sgouezel added awaiting-author A reviewer has asked the author a question or requested changes t-analysis Analysis (normed *, calculus) and removed awaiting-review The author would like community review of the PR labels Jan 19, 2023
loefflerd and others added 4 commits January 19, 2023 14:54
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Here's a new version. I made the changes you suggested, and also split off Gamma_one : Gamma 1 = 1 into a separate lemma for convenience.

@loefflerd loefflerd added awaiting-review The author would like community review of the PR and removed awaiting-author A reviewer has asked the author a question or requested changes labels Jan 19, 2023
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bors r+
Thanks!

@github-actions github-actions bot added the ready-to-merge All that is left is for bors to build and merge this PR. (Remember you need to say `bors r+`.) label Jan 20, 2023
@github-actions github-actions bot removed the awaiting-review The author would like community review of the PR label Jan 20, 2023
bors bot pushed a commit that referenced this pull request Jan 20, 2023
Add the characterisation of the Gamma function as the unique log-convex function with the correct functional equation.
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bors bot commented Jan 20, 2023

Pull request successfully merged into master.

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@bors bors bot changed the title feat(special_functions/gamma): Bohr-Mollerup theorem [Merged by Bors] - feat(special_functions/gamma): Bohr-Mollerup theorem Jan 20, 2023
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@bors bors bot deleted the DL_bohr_mollerup branch January 20, 2023 08:39
bors bot pushed a commit that referenced this pull request Jan 26, 2023
…ction (#18246)

Show (using the log-convexity results proved in #18188) that Gamma is strictly increasing for `2 ≤ x`.
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