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XI.—The Zeta Function of Jacobi. A seven-decimal table of Z(u/m) at interval 0·01 for u and for values of m(= k2) from 0·1 to 1·0

Published online by Cambridge University Press:  15 September 2014

L. M. Milne-Thomson
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Extract

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.

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 52 , 1933 , pp. 236 - 250
Copyright
Copyright © Royal Society of Edinburgh 1933

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References

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