tiIndex level numbers or names, and values should
        be string or callable, as above.

        The default formatter currently expresses floats and complex numbers with the
        pandas display precision unless using the ``precision`` argument here. The
        default formatter does not adjust the representation of missing values unless
        the ``na_rep`` argument is used.

        The ``level`` argument defines which levels of a MultiIndex to apply the
        method to. If the ``formatter`` argument is given in dict form but does
        not include all levels within the level argument then these unspecified levels
        will have the default formatter applied. Any levels in the formatter dict
        specifically excluded from the level argument will be ignored.

        When using a ``formatter`` string the dtypes must be compatible, otherwise a
        `ValueError` will be raised.

        .. warning::
           `Styler.format_index` is ignored when using the output format
           `Styler.to_excel`, since Excel and Python have inherrently different
           formatting structures.
           However, it is possible to use the `number-format` pseudo CSS attribute
           to force Excel permissible formatting. See documentation for `Styler.format`.

        Examples
        --------
        Using ``na_rep`` and ``precision`` with the default ``formatter``

        >>> df = pd.DataFrame([[1, 2, 3]], columns=[2.0, np.nan, 4.0])
        >>> df.style.format_index(axis=1, na_rep='MISS', precision=3)  # doctest: +SKIP
            2.000    MISS   4.000
        0       1       2       3

        Using a ``formatter`` specification on consistent dtypes in a level

        >>> df.style.format_index('{:.2f}', axis=1, na_rep='MISS')  # doctest: +SKIP
             2.00   MISS    4.00
        0       1      2       3

        Using the default ``formatter`` for unspecified levels

        >>> df = pd.DataFrame([[1, 2, 3]],
        ...     columns=pd.MultiIndex.from_arrays([["a", "a", "b"],[2, np.nan, 4]]))
        >>> df.style.format_index({0: lambda v: v.upper()}, axis=1, precision=1)
        ...  # doctest: +SKIP
                       A       B
              2.0    nan     4.0
        0       1      2       3

        Using a callable ``formatter`` function.

        >>> func = lambda s: 'STRING' if isinstance(s, str) else 'FLOAT'
        >>> df.style.format_index(func, axis=1, na_rep='MISS')
        ...  # doctest: +SKIP
                  STRING  STRING
            FLOAT   MISS   FLOAT
        0       1      2       3

        Using a ``formatter`` with HTML ``escape`` and ``na_rep``.

        >>> df = pd.DataFrame([[1, 2, 3]], columns=['"A"', 'A&B', None])
        >>> s = df.style.format_index('$ {0}', axis=1, escape="html", na_rep="NA")
        ...  # doctest: +SKIP
        <th .. >$ &#34;A&#34;</th>
        <th .. >$ A&amp;B</th>
        <th .. >NA</td>
        ...

        Using a ``formatter`` with LaTeX ``escape``.

        >>> df = pd.DataFrame([[1, 2, 3]], columns=["123", "~", "$%#"])
        >>> df.style.format_index("\\textbf{{{}}}", escape="latex", axis=1).to_latex()
        ...  # doctest: +SKIP
        \begin{tabular}{lrrr}
        {} & {\textbf{123}} & {\textbf{\textasciitilde }} & {\textbf{\$\%\#}} \\
        0 & 1 & 2 & 3 \\
        \end{tabular}
        r