If, after constructing a difference table, no clear pattern emerges, turn the paper through an angle of and compute a new table. If necessary, repeat the process. Each rotation reduces powers by 1, so the sequence multiplied by any polynomial in is reduced to 0s by a -fold difference fan.

Call Jackson's difference fan sequence transform the -transform, and define as the -th -transform of the sequence , where and are complex numbers. This is denoted

When , this is known as the binomial transform of the sequence. Greater values of give greater depths of this fanning process.

The inverse -transform of the sequence is given by

When , this gives the inverse binomial transform of .