ASCII math notation

A notation widely used on Internet sites, for example here, where typing complicated mathematical symbols is rather cumbersome.

Long-hand:

ef(x,y,...)

Short-hand:

exp(f(x,y,...))

Long-hand:

lim
    (f(r,x,...))
r->c

Short-hand:

lim(f(r,x,...),r,c)

where c can be a finite quantity, or &inf;. The limit from the left is called llim, and the limit from the right rlim.

Long-hand:

  b
∑ f(x,r,...)
 r=a

Short-hand:

sum(f(x,r,...),r,a,b)

Long-hand:

The Taylor series of degree k for f(x,y,...) with respect to x about a.

Short-hand:

tayl(f(x,y,...),x,k,a)

Long-hand:

The Maclaurin series of degree k for f(x,y,...) with respect to x.

Short-hand:

macl(f(x,y,...),x,k)

Long-hand:

  b
∫ f(x) dx
  a

Short-hand:

int(f(x),x,a,b)

Long-hand:

 d
--- (f(x))
d x

Short-hand:

d/dx(f(x))