is there a polynomial that is oscillatory?

Question

and is there a function defined on an interval [a,b] that is oscillatory?

If there is plenty, can you give an example? please

Answer 1

Not quite sure what you mean by 'oscillatory', but I'm guessing you actually mean 'periodic'.
And yes, there are lots of them. The Fundamental Theorem of Algebra guarantees that, for n specified points in a plane, there will be at -least- one polynomial of order n-1 which passes through them.
Functions on the closed interval [a,b]? Sure. How about the trig functions? (with [a,b] suitably normalized against 2π)

Doug

Answer 2

What about the Taylor serie of sin x?

Ana