These tables, which are based on Jacobi’s parameter q, are intended for numerical calculations with elliptic functions. Previous tables have used Legendre’s modulus Θ. The tables I and II contain functions which are connected with the Jacobian elliptic functions sn u, cn u and dn u; they are especially important in practical work. In tables III and IV there are introduced two new auxiliary functions G̅ and H̅, from which the four theta functions can be obtained by simple calculations. Table V affords conversion between Legendre’s modulusΘ and Jacobi’s parameter q. All these functions are presented to the 5 th decimal place. Finally, in table VI an auxiliary table is given which makes it easy to apply Everett’s interpolation method.
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