Translation of Index Variable of Product

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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 $j$.


Proof




Also see


Sources