- Title
- Transcendental solutions of a class of minimal functional equations
- Creator
- Coons, Michael
- Relation
- Canadian Mathematical Bulletin Vol. 56, p. 283-291
- Publisher Link
- http://dx.doi.org/10.4153/CMB-2011-157-x
- Publisher
- Canadian Mathematical Society
- Resource Type
- journal article
- Date
- 2013
- Description
- We prove a result concerning power series f(z) ∈ ℂ [[z]] satisfying a functional equation of the form [formula could not be replicated] where Ak(z) ∈ ℂ [z]. In particular, we show that if f(z) satisfies a minimal functional equation of the above form with n ≥ 2, then f(z) is necessarily transcendental. Towards a more complete classification, the case n = 1 is also considered.
- Subject
- transcendence; generating functions; Mahler-type functional equation
- Identifier
- http://hdl.handle.net/1959.13/1356961
- Identifier
- uon:31836
- Identifier
- ISSN:0008-4395
- Language
- eng
- Reviewed
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