Apply Function on DataFrame Index

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As already suggested by HYRY in the comments, Series.map is the way to go here. Just set the index to the resulting series.

Simple example:

df = pd.DataFrame({'d': [1, 2, 3]}, index=['FOO', 'BAR', 'BAZ'])
df
        d
FOO     1
BAR     2
BAZ     3

df.index = df.index.map(str.lower)
df
        d
foo     1
bar     2
baz     3

Index != Series

As pointed out by @OP. the df.index.map(str.lower) call returns a numpy array.
This is because dataframe indices are based on numpy arrays, not Series.

The only way of making the index into a Series is to create a Series from it.

pd.Series(df.index.map(str.lower))

Caveat

The Index class now subclasses the StringAccessorMixin, which means that you can do the above operation as follows

df.index.str.lower()

This still produces an Index object, not a Series.

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