the Gamma function

[IshiguroYoshihiro]

Motivation for this change

This PR contains the formalization of the Gamma function. This PR is over #1674 and #1761.

Checklist

• [x] added corresponding entries in CHANGELOG_UNRELEASED.md

• [x] added corresponding documentation in the headers

Reference: How to document

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• PRs with disorganized commits are very likely to be squash-rebased.

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