On the Co-Efficients in the Expansion of cn (x,k)

Hancock in his Theory of Elliptic Functions, Vol. I, page 252, gives the first five co-efficients in the expansion of cn (x,k), as having been calculated by Gudermann in Crelle, Bd. XIX, p. 80. The authors pointed out in their paper : "Determinants involving Specified Numbers," Vol. XIV, No. 4, J. I. M. S., pp. 122-138, that the ascending Σ-table formed with a_2n-1 = (2n-1)², a_2n = (2n)²k² gives the co-efficients in the expansion of cn(x,k) and that with a_2n-1 = (2n-1)²k², a_2n = (2n)² gives the co-efficients in the expansion of dn (x,k)-Ibid, pp. 133, § 6.