Displaying similar documents to “A hybrid of Darboux's method and singularity analysis in combinatorial asymptotics.”

On the sum of digits of some sequences of integers

Javier Cilleruelo, Florian Luca, Juanjo Rué, Ana Zumalacárregui (2013)

Open Mathematics

Similarity:

Let b ≥ 2 be a fixed positive integer. We show for a wide variety of sequences {a n}n=1∞ that for almost all n the sum of digits of a n in base b is at least c b log n, where c b is a constant depending on b and on the sequence. Our approach covers several integer sequences arising from number theory and combinatorics.

Growth orders occurring in expansions of Hardy-field solutions of algebraic differential equations

John Shackell (1995)

Annales de l'institut Fourier

Similarity:

We consider the asymptotic growth of Hardy-field solutions of algebraic differential equations, e.g. solutions with no oscillatory component, and prove that no ‘sub-term’ occurring in a nested expansion of such can tend to zero more rapidly than a fixed rate depending on the order of the differential equation. We also consider series expansions. An example of the results obtained may be stated as follows. Let g be an element of a Hardy field which has an asymptotic series...

Asymptotic values and the growth of analytic functions in spiral domains.

James E. Brennan, Alexander L. Volberg (1993)

Publicacions Matemàtiques

Similarity:

In this note we present a simple proof of a theorem of Hornblower which characterizes those functions analytic in the open unit disk having asymptotic values at a dense set in the boundary. Our method is based on a kind of ∂-mollification and may be of use in other problems as well.