[dingleberry]

i can't think of use of 'if' in a math function; however, if is implicitly used in input, say 0<x<1, f(x)=x, 1<x<3, f(x)=x^2

i see a lot of loop though, summation is so a double integral is loop within loop. i can't think a code analogue with derivative

fta, i take that if in function body makes an ugly code.

[gmfawcett]

Lots of math functions are defined with 'if' -- the absolute value, the Heaviside step function, etc.

[samastur]

That's because you are thinking of continuous functions. You have actually gave an example of a non-continuous one, it's just that you think of it as two functions connected with input conditional.

Other replier already gave you some common example, but let me add another one: signum(x), which returns if number is negative, positive or zero.