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Published online by Cambridge University Press: 15 September 2014
The elliptic integral of the second kind
can, by substitution, be made to depend upon
Writing E(K) = E, Jacobi's Zeta function is defined by
where
Z(u) is an odd function of u with period 2K.
page 236 note * Whittaker, and Watson, , Modern Analysis, 22·73.Google Scholar
page 236 note † Milne-Thomson, L. M., Proc. London Math. Soc., (2) 33 (1931).Google Scholar
page 236 note ‡ For five-figure tables of sn u, cn u, dn u, see Milne-Thomson, , Die elliptischen Funktionen von Jacobi, Berlin, Julius Springer, 1931.CrossRefGoogle Scholar
page 236 note § Whittaker and Robinson, Calciava of Observations, ch. vii.
page 237 note * Milne-Thomson, L. M., Journal London Math. Soc., 5 (1930), p. 148.CrossRefGoogle Scholar
