Associated function

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of a complex variable

A function which is obtained in some manner from a given function with the aid of some fixed function . For example, if

is an entire function and if

is a fixed entire function with , , then

is a function which is associated to by means of the function ; it is assumed that the series converges in some neighbourhood . The function is then represented in terms of by the formula

In particular, if

is an entire function of exponential type and , then

is the Borel-associated function of (cf. Borel transform).

How to Cite This Entry:
Associated function. A.F. Leont'ev (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098