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

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DOI:

https://doi.org/10.18311/jims/1924/17630

Abstract

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 a2n-1 = (2n-1)2, a2n = (2n)2k2 gives the co-efficients in the expansion of cn(x,k) and that with a2n-1 = (2n-1)2k2, a2n = (2n)2 gives the co-efficients in the expansion of dn (x,k)-Ibid, pp. 133, § 6.