The Art of Mathematics

# ∏ or Prod — product of series

## 1. Interface

Full version of the command looks like:

``∏(index, start, finish, step, expression);``

or:

``Prod(index, start, finish, step, expression);``

where index is product index, start — index start value, finish — index finish value (inclusive), step — index step, expression — expression to evaluate for every index value and multiply by. If the index step is 1, which is usually the case, it could be omitted:

``∏(index, start, finish, expression);``

## 2. How to use

For instance:

``∏(k, 2, 8, sin(k));``

is equivalent to

``sin(2)*sin(3)*sin(4)*sin(5)*sin(6)*sin(7)*sin(8)``

and

``Prod(k, 2, 8, 2, sin(k));``

is equivalent to

``sin(2)*sin(4)*sin(6)*sin(8)``

Double product can be written down as nested ones:

``∏(k, 1, 2, ∏(n, 3, 4, k+n));``

which is equivalent of

``(1+3)*(1+4)*(2+3)*(2+4)``

If step parameter is used, its sign makes no difference — step sign always evaluated from comparison of start and finish, if start is greater, the step sign is positive, if finish is greater than start then step sign is negative.

## 3. Support

Product of series is supported in professional version of the Librow calculator.