• ← Integer
• → Rational

Product (∏)

Direct product (SymPy, WMA)

Product[f, {i, $i_{min}$, $i_{max}$}]

evaluates the discrete product of f with i ranging from $i_{min}$ to $i_{max}$.

Product[f, {i, $i_{max}$}]

same as Product[f, {$i, 1, i_{max}$}].

Product[f, {$i, i_{min}, i_{max}$, di}]

i ranges from $i_{min}$ to $i_{max}$ in steps of di.

Product[f, {$i, i_{min}, i_{max}$}, {$j, j_{min}, j_{max}$}, ...]

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

Product[k, {k, i, n}] is defined in terms of Factorial:

• • Product[k, {k, i, n}]

When i is 1, we get the factorial function:

• • Product[k, {k, 1, n}]

Or more succinctly:

• • Product[k, {k, n}]

Symbolic products involving the factorial are evaluated:

• • Product[k, {k, 3, n}]

Examples of numeric evaluation using more complex functions:

• • Product[x^k, {k, 2, 20, 2}]

• • Product[2 ^ i, {i, 1, n}]

• • Product[f[i], {i, 1, 7}]

Evaluate the n-th Primorial:

• • Primorial[0] = 1;

• • Primorial[n_Integer] := Product[Prime[k], {k, 1, n}];

• • Primorial[12]