def METHOD_NAME(string, idx_list):
    """Identify the BibTeX entry identifier before each entry.
    The purpose of this function is to take the raw BibTeX string and a list of indices of entries,
    starting and ending with the braces of each entry, and then extract the identifier before each.
    Parameters
    ----------
    string : :obj:`str`
        The full BibTeX file, as a string.
    idx_list : :obj:`list` of :obj:`tuple` of :obj:`int`
        A list of two-element tuples of indices of matched braces corresponding to BibTeX entries.
    Returns
    -------
    idx_list : :obj:`list` of :obj:`tuple` of :obj:`int`
        A list of two-element tuples of indices of BibTeX entries,
        from the starting @ to the final }.
    """
    at_idx = [(a.start(), a.end() - 1) for a in re.finditer("@[a-zA-Z0-9]+{", string)]
    df = pd.DataFrame(at_idx, columns=["real_start", "false_start"])
    df2 = pd.DataFrame(idx_list, columns=["false_start", "end"])
    df = pd.merge(left=df, right=df2, left_on="false_start", right_on="false_start")
    new_idx_list = list(zip(df.real_start, df.end))
    return new_idx_list