Translation of Index Variable of Product

Theorem

 * $\ds \prod_{\map R j} a_j = \prod_{\map R {c \mathop + j} } a_{c \mathop + j} = \prod_{\map R {c \mathop - j} } a_{c \mathop - j}$

where:
 * $\ds \prod_{\map R j} a_j$ denotes the product over $a_j$ for all $j$ that satisfy the propositional function $\map R j$
 * $c$ is an integer constant which is not dependent upon $j$.

Also see

 * Translation of Index Variable of Summation