Associated function
From Encyclopedia of Mathematics
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
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is an entire function and if
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is a fixed entire function with ,
, then
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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
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In particular, if
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is an entire function of exponential type and , then
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is the Borel-associated function of (cf. Borel transform).
How to Cite This Entry:
Associated function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Associated_function&oldid=45229
Associated function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Associated_function&oldid=45229
This article was adapted from an original article by A.F. Leont'ev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article