Difference between revisions of "Delta spq"
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(Created page with "Let $\mathbb{T}$ be a time scale and let $p$ and $q$ be rd-continuous functions that satisfy the relation $2p(t)+\mu(t)(p(t)^2+q(t)^2)=0$. The (alternative) delta sine fun...") |
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$$s_{pq}(t,s) = \dfrac{e_{p+iq}(t,s)-e_{p-iq}(t,s)}{2i},$$ | $$s_{pq}(t,s) = \dfrac{e_{p+iq}(t,s)-e_{p-iq}(t,s)}{2i},$$ | ||
where $e_{p+iq}$ denotes the [[delta exponential]]. | where $e_{p+iq}$ denotes the [[delta exponential]]. | ||
| + | |||
| + | =Properties= | ||
| + | [[Pythagorean identity for alternate delta trigonometric functions]]<br /> | ||
| + | [[Derivative of alternative delta cosine]]<br /> | ||
| + | [[Derivative of alternative delta sine]]<br /> | ||
=See Also= | =See Also= | ||
[[Delta cpq]]<br /> | [[Delta cpq]]<br /> | ||
Latest revision as of 00:43, 15 September 2016
Let $\mathbb{T}$ be a time scale and let $p$ and $q$ be rd-continuous functions that satisfy the relation $2p(t)+\mu(t)(p(t)^2+q(t)^2)=0$. The (alternative) delta sine function is defined by $$s_{pq}(t,s) = \dfrac{e_{p+iq}(t,s)-e_{p-iq}(t,s)}{2i},$$ where $e_{p+iq}$ denotes the delta exponential.
Properties
Pythagorean identity for alternate delta trigonometric functions
Derivative of alternative delta cosine
Derivative of alternative delta sine
