# Difference between revisions of "Relationship between delta hk and delta gk"

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− | + | ==Theorem== Let $\mathbb{T}$ be a [[time scale]], let $t,s \in \mathbb{T}$, and let $k$ be a nonnegative integer. Then the following formula holds: | |

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$$h_k(t,s;\mathbb{T})=(-1)^kg_k(s,t;\mathbb{T}),$$ | $$h_k(t,s;\mathbb{T})=(-1)^kg_k(s,t;\mathbb{T}),$$ | ||

where $h_k$ denotes the [[delta hk]] and $g_k$ denotes the [[delta gk]]. | where $h_k$ denotes the [[delta hk]] and $g_k$ denotes the [[delta gk]]. | ||

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− | + | ==Proof== | |

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− | + | ==References== | |

+ | |||

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

+ | [[Category:Unproven]] |

## Revision as of 01:59, 10 June 2016

==Theorem== Let $\mathbb{T}$ be a time scale, let $t,s \in \mathbb{T}$, and let $k$ be a nonnegative integer. Then the following formula holds: $$h_k(t,s;\mathbb{T})=(-1)^kg_k(s,t;\mathbb{T}),$$ where $h_k$ denotes the delta hk and $g_k$ denotes the delta gk.