Delta spq

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