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An Entire Function Defined by a Nonlinear Recurrence Relation
Author(s) -
Hone A. N. W.,
Joshi N.,
Kitaev A. V.
Publication year - 2002
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610702003423
Subject(s) - recurrence relation , nonlinear system , mathematics , relation (database) , function (biology) , limit (mathematics) , combinatorics , mathematical analysis , pure mathematics , physics , quantum mechanics , computer science , biology , database , evolutionary biology
For the nonlinear recurrence relationα 2 = α 1 ( 1 − α 1 ) ,α k + 1 = k 2 α k + ∑ m = 2 k − 1α m α k + 1 − m ,k ⩾ 2 ,it is proved that the limitp ∞ ( α 2 ) = lim k → ∞α k /[( k − 1 ) ! ] 2exists and defines an entire function of α 2 = α 1 (1‐α 1 ).