## The new encyclopaedia Britannica: in 32 vol. Macropaedia, Accounting - Architecture, Volume 13 |

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Page 464

The residue theorem also plays a central role in the theory of elliptic

112) f(z)dz = 2nila_u ... This theorem, proved by Picard in 1879 by use of the

elliptic modular

Elementary ...

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.Elementary ...

Page 494

A real finite continuous

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),

...

A real finite continuous

**function**u on an open set co is said to be harmonic, if it isequal 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),

...

Page 502

If / is a

defined (see 511). A somewhat more general example arises if /is multiplied by

another

a to ...

If / is a

**function**defined on the interval [a, b], a new**function**F on [a, b] can bedefined (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 froma to ...

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