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In [1]: import pandas as pd
   ...: mapping = pd.DataFrame({'day': ['Sun', 'Mon', 'Tue', 'Wed', 'Thu', 'Fri', 'Sat'], 'daynum': range(1, 8)})
   ...: print(mapping)
   day  daynum
0  Sun       1
1  Mon       2
2  Tue       3
3  Wed       4
4  Thu       5
5  Fri       6
6  Sat       7

In [2]: df = pd.DataFrame({'x': [5, 2, 7, 0, 1, 8], 'y': [59, 63, 66, 61, 46, 66]})
   ...: print(df)
   x   y
0  5  59
1  2  63
2  7  66
3  0  61
4  1  46
5  8  66

In [3]: df['z'] = df['x'].map(mapping.set_index('daynum')['day'])
   ...: print(df)
   x   y    z
0  5  59  Thu
1  2  63  Mon
2  7  66  Sat
3  0  61  NaN
4  1  46  Sun
5  8  66  NaN

See also: https://stackoverflow.com/questions/46049658/mapping-columns-from-one-dataframe-to-another-to-create-a-new-column - shows other possible solutions