# Difference between revisions of "Delta simple useful formula"

From timescalewiki

Line 7: | Line 7: | ||

==References== | ==References== | ||

− | * {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=Delta derivative at right-dense|next=Delta derivative of sum}}: Theorem 1. | + | * {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=Delta derivative at right-dense|next=Delta derivative of sum}}: Theorem 1.16 (iv) |

[[Category:Theorem]] | [[Category:Theorem]] | ||

[[Category:Unproven]] | [[Category:Unproven]] |

## Latest revision as of 06:08, 10 June 2016

## Theorem

Let $\mathbb{T}$ be a time scale, let $t,s \in \mathbb{T}$, and $p \in \mathcal{R} \left( \mathbb{T},\mathbb{C} \right)$ be a regressive function. The following formula holds: $$e_p(\sigma(t),s;\mathbb{T})=(1+\mu(t)p(t))e_p(t,s;\mathbb{T}),$$ where $e_p$ denotes the delta exponential, $\sigma$ denotes the forward jump, and $\mu$ denotes the forward graininess.

## Proof

## References

- Martin Bohner and Allan Peterson:
*Dynamic Equations on Time Scales*(2001)... (previous)... (next): Theorem 1.16 (iv)