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

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Page 464

Cauchy's theorem (see 108) must be modified if f(z) is not holomorphic inside C.

If the only singularities are isolated and none lies on C, then the integral of the

...

Cauchy's theorem (see 108) must be modified if f(z) is not holomorphic inside C.

If the only singularities are isolated and none lies on C, then the integral of the

**function**around the curve is expressed in terms of a sum (see 1 12), in which the...

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

HARMONIC ANALYSIS AND INTEGRAL TRANSFORMS It usually happens in

mathematical analysis that certain given

other

...

HARMONIC ANALYSIS AND INTEGRAL TRANSFORMS It usually happens in

mathematical analysis that certain given

**functions**are to be operated on, andother

**functions**or numbers are thus obtained. Often, the operations used involve...

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