Abstract
The paper is devoted to the study of expansions of functions ƒ, which are holomorphic in a circle Ω around 0, in a series of the form 
where the given system of functions (fk)
℞k=0
has the property that each function fk has a representation as a power series of the form 
with a
(k)0
= 1. It is the question if and where an expansion of the form (*) holds. We present sufficient conditions for the sequence (a
(k)n
)
∞k,n=0
, under which there exists a subset Ω0 of Ω such that for arbitrary ƒ the expansion (*) holds on Ω0 and the series converges absolutely uniformly on compact subsets of Ω0.
The obtained results can be applied to prove expansions of analytic functions in a series of a suitable system of m-fold products of Bessel functions. Expansions of this type have been treated by many authors in special cases, but we are able to state a general expansion theorem.
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Saurer, J. Expansions in Series of Suitable Systems of Functions. Results. Math. 41, 369–385 (2002). https://doi.org/10.1007/BF03322779
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DOI: https://doi.org/10.1007/BF03322779