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22 Jacobian Elliptic FunctionsComputation

§22.21 Tables

Spenceley and Spenceley (1947) tabulates sn(Kx,k), cn(Kx,k), dn(Kx,k), am(Kx,k), (Kx,k) for arcsink=1(1)89 and x=0(190)1 to 12D, or 12 decimals of a radian in the case of am(Kx,k).

Curtis (1964b) tabulates sn(mK/n,k), cn(mK/n,k), dn(mK/n,k) for n=2(1)15, m=1(1)n1, and q (not k) =0(.005)0.35 to 20D.

Lawden (1989, pp. 280–284 and 293–297) tabulates sn(x,k), cn(x,k), dn(x,k), (x,k), Z(x|k) to 5D for k=0.1(.1)0.9, x=0(.1)X, where X ranges from 1.5 to 2.2.

Zhang and Jin (1996, p. 678) tabulates sn(Kx,k), cn(Kx,k), dn(Kx,k) for k=14,12 and x=0(.1)4 to 7D.

For other tables prior to 1961 see Fletcher et al. (1962, pp. 500–503) and Lebedev and Fedorova (1960, pp. 221–223).

Tables of theta functions (§20.15) can also be used to compute the twelve Jacobian elliptic functions by application of the quotient formulas given in §22.2.