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

See Also

Delta cpq