Calculate a Double Product
Calculator for double products, the connections of two products, an inner and an outer product. The inner product with the running variable j runs from o to p, the outer product with the running variable i from m to n. Only the variables i and j may occur in the sum term. The basic arithmetic operations + - * / are allowed, as well as the power function, like pow(j#i) for ji. Further allowed functions are sin(), cos(), tan(), asin(), acos(), atan(), log() for the natural logarithm and fac() for the factorial. Also, the constants e and pi can be used. If i≠j is chosen, factors with equal running variables are omitted. The double product can quickly lead to very high values.
A double product is calculated by first calculating the complete inner product from j=o to j=p for i=m. The inner product is then calculated again completely for i=m+1 and multiplied with the previous intermediate result, and so on until i=n.
Output in a table is probably the clearest and, for many purposes, most useful form. From left to right, j is incremented by one with each step, and from top to bottom, i is incremented by one with each step. When outputting in a row, two lines are written one below the other: steps i and j at the top, and the intermediate values down to the final result at the bottom. This output can, of course, become very long. Additionally, with the double product, the results can very quickly become very large, resulting in correspondingly long fields in the table cells. Therefore, (i+j)/4 was chosen as the example formula; dividing by four noticeably slows down the rapid growth, compared to i+j.
Retrieved on 2026-07-16 from https://rechneronline.de/sum/double-product.php
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