'To revert a series' definitions:

Definition of 'To revert a series'

From: GCIDE

Revert \Re*vert"\, v. t. [imp. & p. p. Reverted; p. pr. & vb. n. Reverting.] [L. revertere, reversum; pref. re- re- + vertere to turn: cf. OF. revertir. See Verse, and cf. Reverse.]
1. To turn back, or to the contrary; to reverse. [1913 Webster]
Till happy chance revert the cruel scence. --Prior. [1913 Webster]
The tumbling stream . . . Reverted, plays in undulating flow. --Thomson. [1913 Webster]
2. To throw back; to reflect; to reverberate. [1913 Webster]
3. (Chem.) To change back. See Revert, v. i. [1913 Webster]
To revert a series (Alg.), to treat a series, as y = a + bx + cx^2 + etc., where one variable y is expressed in powers of a second variable x, so as to find therefrom the second variable x, expressed in a series arranged in powers of y. [1913 Webster]