pip using out of date package index
Two possibilities:

the package needs you to use an underscore (since hyphens don't behave) so pip can download it: so run pip install azureml_core==1.13.0
Run with the --no-cache-dir argument, so pip install --no-cache-dir azureml_core==1.13.0. This argument forces pip to refresh it's package cache.
I am trying to install package inside a docker container(python:rc-slim).
As of now I see that most recent azureml-core wheel uploaded to PyPI is:

azureml_core-1.13.0-py3-none-any.whl

but when I run pip install azureml-core==1.13.0 I get following error:

ERROR: Could not find a version that satisfies the requirement
azureml-core==1.13.0 (from versions: 0.1.50, 0.1.57, 0.1.58, 0.1.59,
0.1.65, 0.1.68, 0.1.74, 0.1.80, 1.0rc83, 1.0rc85, 1.0.2, 1.0.6, 1.0.8, 1.0.10, 1.0.15, 1.0.17, 1.0.17.1, 1.0.18, 1.0.21, 1.0.23, 1.0.30, 1.0.33, 1.0.33.1, 1.0.39, 1.0.41, 1.0.41.1, 1.0.43, 1.0.43.1, 1.0.45, 1.0.48, 1.0.53, 1.0.55, 1.0.57, 1.0.57.1, 1.0.60, 1.0.62, 1.0.62.1, 1.0.65, 1.0.65.1, 1.0.69, 1.0.72, 1.0.74, 1.0.76, 1.0.76.1, 1.0.79, 1.0.81, 1.0.81.1, 1.0.83, 1.0.85, 1.0.85.1, 1.0.85.2, 1.0.85.3, 1.0.85.4, 1.0.85.5, 1.0.85.6, 1.1.0rc0, 1.1.1rc0, 1.1.1.1rc0, 1.1.1.2rc0, 1.1.2rc0, 1.1.5, 1.1.5.1, 1.1.5.2, 1.1.5.3, 1.1.5.4, 1.1.5.5, 1.1.5.6, 1.1.5.7)

When installing packages from 'apt-get' I usually have to update the index first but I can't find a comparable command to do that with pip.