Product

Product(expr, {i, imin, imax})

evaluates the discrete product of expr with i ranging from imin to imax.

Product(expr, {i, imin, imax, di})

i ranges from imin to imax in steps of di.

Product(expr, {i, imin, imax}, {j, jmin, jmax}, ...)

evaluates expr as a multiple sum, with {i, ...}, {j, ...}, ... being in outermost-to-innermost order.

See

>> Product(k, {k, 1, 10})
3628800

>> 10!
3628800

>> Product(x^k, {k, 2, 20, 2})
x^110

>> Product(2 ^ i, {i, 1, n})
2^(1/2*n*(1+n))

Symbolic products involving the factorial are evaluated:

>> Product(k, {k, 3, n})
n! / 2

Evaluate the nth primorial:

>> primorial(0) = 1;
>> primorial(n_Integer) := Product(Prime(k), {k, 1, n});
>> primorial(12)
7420738134810