# Multisectioning, Rational Poly-Exponential Functions and Parallel Computation

Hare, Kevin G. (1999) Multisectioning, Rational Poly-Exponential Functions and Parallel Computation. MSc Thesis thesis, Simon Fraser University.

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Bernoulli numbers and similar arithmetic objects have long been of interest in mathematics. Historically, people have been interested in different recursion formulae that can be derived for the Bernoulli numbers, and the use of these recursion formulae for the calculation of Bernoulli numbers. Some of these methods, which in the past have only been of theoretical interest, are now practical with the availability of high-powered computation. This thesis explores some of these techniques of deriving new recursion formulae, and expands upon these methods. The main technique that is explored is that of {\em multisectioning}''. Typically, the calculation of a Bernoulli number requires the calculation of all previous Bernoulli numbers. The method of multisectioning is such that only a fraction of the previous Bernoulli numbers are needed. In exchange, a more complicated recursion formula, called a {\em lacunary recursion formula}'', must be derived and used.