# What is the meaning of the math symbol “$\theta$”, as in “$\theta(31\pi-t)\,\theta(t-27\pi)$”?

What would be the meaning of the sign "$$\theta$$" that looks like a slashed zero?

• it is a greek letter named Theta $\theta$. Its used in number theory functins but I don't think that this is the case. – Luis Felipe Jun 16 '20 at 19:25
• Is there a context for this equation? – Alex R. Jun 16 '20 at 19:27
• It’s probably defined earlier in the same place where you found this formula. Where did this come from? – David K Jun 16 '20 at 19:28
• You seem to be using Wolfram and I believe this is the Heaviside Theta function. – Peter Foreman Jun 16 '20 at 19:28
• Thank you Peter Foreman, that was the link I needed. – Emmanuel Pil Jun 16 '20 at 19:59

I have seen it used for a unit step function, which is $$1$$ if the argument is positive and $$0$$ if the argument is negative. For most uses you don't care what happens at $$0$$, but it is often taken to be $$\frac 12.$$ In your example, the expression would be $$0$$ outside the interval $$[27\pi, 31\pi]$$ and the theta functions would multiply to $$1$$ within that interval and $$\frac 12$$ at the endpoints.