A 20-D table of Jacobi's nome and its inverse

Author / Creator

Fettis, Henry E., author

Available as

Online

Summary

Jacobi's Nome q is given to twenty decimals as a function of the modulus-squared, k squared, the modular angle arc sin k, and the complementary modulus k' for k squared : 0(.001) 999; arc sin k : 0...

Jacobi's Nome q is given to twenty decimals as a function of the modulus-squared, k squared, the modular angle arc sin k, and the complementary modulus k' for k squared : 0(.001) 999; arc sin k : 0(.10) 89 degrees (.01) 89.99 degrees (.0002) 90 degrees; k' : 0001(.0001).02. The latter table also gives values of an approximation valid in this range to the order of (k') squared, as well as the ratio of the true and approximate values and second central differences of the latter ratio. The fourth table gives k and k' as functions of q for q = 0(.001).5.

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