Calculate a Double Sum

Calculator for double sums, the connections of two sums, an inner and an outer sum. The inner sum with the running variable j runs from o to p, the outer sum 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, summands with equal running variables are omitted.

A double sum is calculated by first calculating the complete inner sum from j=o to j=p for i=m. The inner sum is then calculated again completely for i=m+1 and added to 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.

There are a few special applications for double sums. Euler numbers, which are different from Euler's number but related to it, can be calculated using complicated double sums. Instead of writing a summation symbol twice, you can of course also write it multiple times in a row, resulting in triple sums, quadruple sums, and so on. This will, of course, become increasingly confusing and computationally intensive, and the practical applications will likely become increasingly less. But theoretically, there are no limits to what can be done.