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The residue theorem also plays a central role in the theory of elliptic functions. » (
112) f(z)dz = 2nila_u ... This theorem, proved by Picard in 1879 by use of the
elliptic modular function, has been in the centre of attention ever since.
A real finite continuous function u on an open set co is said to be harmonic, if it is
equal at each point x to its mean value on any ball (that is, a disc in 9t2) B* (
centre x, radius r), or equivalently (using the corresponding Lebesgue measure),
If / is a function defined on the interval [a, b], a new function F on [a, b] can be
defined (see 511). A somewhat more general example arises if /is multiplied by
another function h(y) before integrating: F is expressed as a definite integral from
a to ...
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This is the 198215th Edition, in two halves, with the Macropaedia and the Micropaedia. First published in 1768, the publisher is the oldest English-language encyclopedia still in print. Two Scottish ... Read full review
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For virtually all its 238 years,Britannica has ruled the shelves as a peerless general encyclopedia. Reviewers have consistently given it high marks for most of the 12 criteria identified inKister's ... Read full review