Docs: add instructions for publishing to JFrog's Artifactory

docs/guides/integration/alternative-indexes.md

@@ -368,6 +368,68 @@ $ uv publish
 Note this method is not preferable because uv cannot check if the package is already published
 before uploading artifacts.
 
-## Other package indexes
+## JFrog Artifactory
 
-uv is also known to work with JFrog's Artifactory.
+uv can install packages from JFrog Artifactory, either by using a username and password or a JWT
+token.
+
+To use it, add the index to your project:
+
+```toml title="pyproject.toml"
+[[tool.uv.index]]
+name = "private-registry"
+url = "https://<organization>.jfrog.io/artifactory/api/pypi/<repository>/simple"
+```
+
+### Authenticate with username and password
+
+```console
+$ export UV_INDEX_PRIVATE_REGISTRY_USERNAME="<username>"
+$ export UV_INDEX_PRIVATE_REGISTRY_PASSWORD="<password>"
+```
+
+### Authenticate with JWT token
+
+```console
+$ export UV_INDEX_PRIVATE_REGISTRY_USERNAME=""
+$ export UV_INDEX_PRIVATE_REGISTRY_PASSWORD="$JFROG_JWT_TOKEN"
+```
+
+!!! note
+
+    Replace `PRIVATE_REGISTRY` in the environment variable names with the actual index name defined in your `pyproject.toml`.
+
+### Publishing packages to JFrog Artifactory
+
+Add a `publish-url` to your index definition:
+
+```toml title="pyproject.toml"
+[[tool.uv.index]]
+name = "private-registry"
+url = "https://<organization>.jfrog.io/artifactory/api/pypi/<repository>/simple"
+publish-url = "https://<organization>.jfrog.io/artifactory/api/pypi/<repository>"
+```
+
+!!! important
+
+    If you use `--token "$JFROG_TOKEN"` or `UV_PUBLISH_TOKEN` with JFrog, you will receive a
+    401 Unauthorized error as JFrog requires an empty username but uv passes `__token__` for as
+    the username when `--token` is used.
+
+To authenticate, pass your token as the password and set the username to an empty string:
+
+```console
+$ uv publish --index <index_name> -u "" -p "$JFROG_TOKEN"
+```
+
+Alternatively, you can set environment variables:
+
+```console
+$ export UV_PUBLISH_USERNAME=""
+$ export UV_PUBLISH_PASSWORD="$JFROG_TOKEN"
+$ uv publish --index private-registry
+```
+
+!!! note
+
+    The publish environment variables (`UV_PUBLISH_USERNAME` and `UV_PUBLISH_PASSWORD`) do not include the index name.