Singularity Analysis and Asymptotics of Bernoulli Sums Singularity Analysis and Asymptotics of Bernoulli Sums Singularity Analysis and Asymptotics of Bernoulli Sums

The asymptotic analysis of a class of binomial sums that arise in information theory can be performed in a simple way by means of singularity analysis of generating functions. The method developed extends the range of applicability of singularity analysis techniques to combinatorial sums involving transcendental elements like logarithms or fractional powers. Analyse de singularit e et asymptotique des sommes de Bernoulli R esum e : L'analyse asymptotique d'une classe de sommes qui interviennent en th eorie de l'information peut ^ etre eeectu ee de mani ere simple par analyse de singularit e de s eries g en eratrices. La m ethode d evelopp ee dans ce rapport etend en fait l'applicabilit e des techniques d'analyse de singularit e a des sommes combinatoires comprenant des el ements tran-scendants tels des logarithmes ou des puissances fractionnaires. Abstract. The asymptotic analysis of a class of binomial sums that arise in information theory can be performed in a simple way by means of singularity analysis of generating functions. The method developed extends the range of applicability of singularity analysis techniques to combinatorial sums involving transcendental elements like logarithms or fractional powers.