# Rational Poly-Exponential Functions - Lucas numbers

## Definition.

The Lucas numbers are defined as the L_{i } in:
The Lucas numbers can be solved by the recurrence relation:
where *m* is the value being multisectioned by, *q* is the
value being multisectioned to, and *s* is specified
below for each particular case of multisectioning.
All of the odd Lucas numbers are 0.
Hence, the only multisectioning of interest, is by an even amount.
Either the recurrences can be used as given below with the formula
above, or code written for this purpose can be used to perform
these calculations.
## Some Recurrences

Some recurrences are worked out for your convenience.
These files are stored as maple ".m" files. The
denominator, when loaded, is the procedure "Bot",
and the numerator, when loaded is the procedure "Top".
- Multisectioning by 2. Here
*s* = 2.
- Multisectioning by 6. Here
*s* = 3.
- Multisectioning by 10. Here
*s* = 5.
- Multisectioning by 12. Here
*s* = 6.
- Multisectioning by 14. Here
*s* = 7.
- Multisectioning by 16. Here
*s* = 8.
- Multisectioning by 18. Here
*s* = 9.
- Multisectioning by 20. Here
*s* = 10.

Send comments to: kghare(at)cecm.sfu.ca
Back

###### This file was last modified *April 14, 1999 *.