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 $j$.


Proof


This theorem requires a proof.
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.
To discuss this page in more detail, feel free to use the talk page.
When this work has been completed, you may remove this instance of {{ProofWanted}} from the code.
If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.



Also see


Sources

  • 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.3$: Sums and Products
This article is issued from ProofWiki. The text is available under Creative Commons Attribution-ShareAlike License unless otherwise noted. Additional terms may apply for the media files.