§23.9 Laurent and Other Power Series

Let be the nearest lattice point to the origin, and define

Then

23.9.2,
23.9.3.

Here

23.9.4
23.9.5.

Explicit coefficients in terms of and are given up to in Abramowitz and Stegun (1964, p. 636).

For , and with as in §23.3(i),

as . For the next four terms see Abramowitz and Stegun (1964, (18.5.56)). Also, Abramowitz and Stegun (1964, (18.5.25)) supplies the first 22 terms in the reverted form of (23.9.2) as .

For

where , if either or , and

23.9.8

For with and , see Abramowitz and Stegun (1964, p. 637).