Event Title

The Central Hankel Transform

Presenter Information

Matthew Levine, Colby CollegeFollow

Location

Diamond 344

Start Date

30-4-2015 11:00 AM

End Date

30-4-2015 11:55 AM

Project Type

Presentation

Description

We define central Hankel matrices, variations on the well-understood Hankel matrices, in order to investigate familiar sequences, e.g. arithmetic, Fibonacci, and Lucas sequences. We find explicit closed formulae for determinant of a central Hankel matrix of these particular sequences that ares closely related to the those of the determinants of particular Toeplitz matrices. These closed formulae lead to new identities for the Fibonacci sequence. We conclude by showing that the Central Hankel Transform can uniquely describe the generalized Fibonacci sequence.

Faculty Sponsor

Ben Mathes

Sponsoring Department

Colby College. Mathematics and Statistics Dept.

CLAS Field of Study

Natural Sciences

Event Website

http://www.colby.edu/clas

ID

1625

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Apr 30th, 11:00 AM Apr 30th, 11:55 AM

The Central Hankel Transform

Diamond 344

We define central Hankel matrices, variations on the well-understood Hankel matrices, in order to investigate familiar sequences, e.g. arithmetic, Fibonacci, and Lucas sequences. We find explicit closed formulae for determinant of a central Hankel matrix of these particular sequences that ares closely related to the those of the determinants of particular Toeplitz matrices. These closed formulae lead to new identities for the Fibonacci sequence. We conclude by showing that the Central Hankel Transform can uniquely describe the generalized Fibonacci sequence.

http://digitalcommons.colby.edu/clas/2015/program/345