Abstract.
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 highpowered
computation.
This project explores some of these techniques of deriving new
recursion formulae, and expands upon these methods.
The main technique that is explored is that of
``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 ``lacunary recursion formula'' must be derived and used.
This page contains some Maple code, help files, and worksheets to
demonstrate how to perform these recurrences.
Documentation.

Multisectioning, Rational PolyExponential functions and Parallel
Computation. (postscript, 167 pages)

Multisectioning, Rational PolyExponential functions and Parallel
Computation. (pdf, 167 pages)
Maple libraries.

April 13, 1999,
maple.lib, Maple Library, Version 1.0,

April 13, 1999,
maple.ind Maple Index, Version 1.0,

April 13, 1999,
maple.hdb Maple Help Database, Version 1.0,
Maple worksheets.
List of worksheets demonstrating this code
Recurrences.

List of recurrences so far derived for the
Bernoulli numbers

List of recurrences so far derived for the
Euler numbers

List of recurrences so far derived for the
Genocchi numbers

List of recurrences so far derived for the
Lucas numbers
Other information
 Additional documentation
Send comments to: kghare(at)cecm.sfu.ca
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This file was last modified April 14, 1999 .