A recent paper (J. Number Theory 42 (1992), 61 87) announced various arithmetical properties of the Mahler function f (%, ,; x, y)= k=1 1 m k%+, x k y m . Unfortunately the arguments of that paper are marred by an error whereby the arguments hold only for ,=0 (or when b n =1 for all positive integer
On the expansion of a function in series and continued fractions
β Scribed by G. Auslender
- Publisher
- Elsevier Science
- Year
- 1963
- Weight
- 283 KB
- Volume
- 3
- Category
- Article
- ISSN
- 0041-5553
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π SIMILAR VOLUMES
Some time ago Mills and Robbins (1986, J. Number Theory 23, No. 3, 388-404) conjectured a simple closed form for the continued fraction expansion of the power series solution \(f=a_{1} x^{-1}+a_{2} x^{-2}+\cdots\) to the equation \(f^{4}+f^{2}-x f+1=0\) when the base field is GF(3). In this paper we
Patterns for simple continued fractions of the analogues of (xe 2Γf +y)Γ(ze 2Γf +w) in the F q [t] case are described. In contrast to the classical case where they consist of arithmetic progressions, in this case they involve an interesting inductive scheme of block repetition and reversals, especia
We show that functions of two complex variables which are symmetric and holomorphic on suitable domains can be expanded in locally uniform convergent series of products of LamΓ© polynomials. The result is based on a more general expansion theorem for holomorphic functions defined on a two-dimensional