§22.21 Tables

Keywords:: Jacobian elliptic functions, Jacobi’s epsilon function, Jacobi’s zeta function, amplitude ( $\mathop{\mathrm{am}\/}\nolimits$ ) function
Permalink:: http://dlmf.nist.gov/22.21

Spenceley and Spenceley (1947) tabulates $\mathop{\mathrm{sn}\/}\nolimits\left(Kx,k\right)$ , $\mathop{\mathrm{cn}\/}\nolimits\left(Kx,k\right)$ , $\mathop{\mathrm{dn}\/}\nolimits\left(Kx,k\right)$ , $\mathop{\mathrm{am}\/}\nolimits\left(Kx,k\right)$ , $\mathop{\mathcal{E}\/}\nolimits\!\left(Kx,k\right)$ for $\mathop{\mathrm{arcsin}\/}\nolimits k=1^{\circ}(1^{\circ})89^{\circ}$ and $x=0\left(\tfrac{1}{90}\right)1$ to 12D, or 12 decimals of a radian in the case of $\mathop{\mathrm{am}\/}\nolimits\left(Kx,k\right)$ .

Curtis (1964b) tabulates $\mathop{\mathrm{sn}\/}\nolimits\left(mK/n,k\right)$ , $\mathop{\mathrm{cn}\/}\nolimits\left(mK/n,k\right)$ , $\mathop{\mathrm{dn}\/}\nolimits\left(mK/n,k\right)$ for $n=2(1)15$ , $m=1(1)n-1$ , and $q$ (not $k$ ) $=0(.005)0.35$ to 20D.

Lawden (1989, pp. 280–284 and 293–297) tabulates $\mathop{\mathrm{sn}\/}\nolimits\left(x,k\right)$ , $\mathop{\mathrm{cn}\/}\nolimits\left(x,k\right)$ , $\mathop{\mathrm{dn}\/}\nolimits\left(x,k\right)$ , $\mathop{\mathcal{E}\/}\nolimits\!\left(x,k\right)$ , $\mathop{\mathrm{Z}\/}\nolimits\!\left(x|k\right)$ 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 $\mathop{\mathrm{sn}\/}\nolimits\left(Kx,k\right)$ , $\mathop{\mathrm{cn}\/}\nolimits\left(Kx,k\right)$ , $\mathop{\mathrm{dn}\/}\nolimits\left(Kx,k\right)$ for $k=\frac{1}{4},\frac{1}{2}$ 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.