A Discourse on Fibonacci Numbers, Extended Series and Governing Equations

The Fibonacci series 1, 1, 2, 3, 5, 8, 13, 21… origin is re-examined and new series are obtained using different constraints. Their governing equations are derived and the effects of constant and series-dependent multipliers are explored. Systems of co-dependent series are studied and mapping of the original Fibonacci series to the newly derived series is established. Single term series are built to address vulnerabilities of the mapped series and special cases of twin series are briefly discussed