# Fourier series coefficent of $Y(2t+1)$?

Suppose the fourier series coefficient of Y(t) is Cn then what will be the fourier series coefficint of Y(2t+1)?

My doubt regarding this is if we do first shifting and then scaling ans will be $e^{jnw}Cn$ but if we do first scaling and the shifting then it will be $e^{0.5jnw)}Cn$

why is my answer changing and what is the correct procedure?

Here both operation will give the same graph

HINT: $$x(t) \Leftrightarrow c_{n}$$ $$x(at) \Leftrightarrow c_{n}$$ On scaling operation Only the frequency will be scaled $a$ times i.e $\omega' \mapsto w.a$ $$x(t \pm t_{0}) \Leftrightarrow c_{n}\cdot e^{\pm j \, k\, \omega_{0}\, t_{0}}$$ operation wise:For $A.y(at \pm t_{0})$ $$y(t) \rightarrow A.y(t) \underbrace{\rightarrow}_{shifting} y(t \pm t_{0}) \underbrace{\rightarrow}_{scaling} y(at \pm t_{0})$$