Finding the power series expansion of function sin (3Z ^ 2)

Finding the power series expansion of function sin (3Z ^ 2)

Directly use Sinz = ∑ [(- 1) ^ N Z ^ (2n + 1)] / (2n + 1)! To sum from 0 to ∞
Σ[(-1)^n(3z²)^(2n+1)]/(2n+1)!
=Σ[(-1)^n(3)^(2n+1)z^(4n+2)]/(2n+1)!