No. Assuming you want ∞ to mean infinity, beware of involving it in any equation. If you want it to mean something else, use another symbol.

Similarly t' can mean t + Δt or anything else you define it as, and σ is usually reserved for standard deviation, unless you define it as something else.

Always begin with your definitions, so people know what you are talking about. As my navigation instructor used to say "start from where you are, then you won't get lost before you take off". When you have landed, tell the passengers where you are - i.e. what you have demonstrated by your mathematics. Maths is the way we plot our course from one physical observation to another!

And remember cos^{2}x + sin^{2}x = 1. This is a great help in checkng your equations and graphs.

For what it's worth, white light is a continuous spectrum. You can't generate it from the harmonics of a single frequency.