Advanced
Supports functions: sin, cos, tan, log, exp, sqrt, abs, min, max, pow.
Result
Computed cells: 9 | i values: 3 | j values: 3
S = Σi=1≤3 Σj=1≤3 f(i,j)
Total sum S = 36.000000
| i \ j | 1 | 2 | 3 | Row sum |
|---|---|---|---|---|
| 1 | 1.000000 | 2.000000 | 3.000000 | 6.000000 |
| 2 | 2.000000 | 4.000000 | 6.000000 | 12.000000 |
| 3 | 3.000000 | 6.000000 | 9.000000 | 18.000000 |
| Column sum | 6.000000 | 12.000000 | 18.000000 | 36.000000 |
Note: Order of summation should match due to Fubini for finite sums.
Formula Used
S = Σi=mn Σj=pq f(i,j),
optionally including only terms where C(i,j) is true.
- Index sets: i ∈ {m, m+Δi, …, n} and j ∈ {p, p+Δj, …, q}.
- Δi and Δj are step sizes; upper bounds may be inclusive.
- Supported functions: sin, cos, tan, log, exp, sqrt, abs, min, max, pow.
- Constants: π via
pi, Euler’s number viae.
How to Use
- Enter the expression
f(i,j)(e.g.,i*j - j^2 + sin(i)). - Set ranges and steps for i and j; choose inclusive bounds as needed.
- Optionally add a condition like
j >= i && (j%2)==0. - Select the summation order and precision; press Compute.
- Download the matrix as CSV, or export a PDF report.
Example Data Table
Example for f(i,j)=i*j, i=1..3, j=1..3, step=1, inclusive bounds.
| i \ j | 1 | 2 | 3 | Row sum |
|---|---|---|---|---|
| 1 | 1 | 2 | 3 | 6 |
| 2 | 2 | 4 | 6 | 12 |
| 3 | 3 | 6 | 9 | 18 |
| Column sum | 6 | 12 | 18 | 36 |
FAQs
Arithmetic +, −, ×, ÷, %, power (^), comparisons, logical &&, ||, and functions sin, cos, tan, asin, acos, atan, log, exp, sqrt, abs, min, max, pow.
Each index has a toggle for including the upper bound. Lower bounds are always included.
Radians. Convert degrees with
sin(x*pi/180) or similar where needed.For finite sums with the same included terms, order independence holds; both orders sum the identical set of terms.
For stability, the calculator limits to 10,000 cells. Reduce ranges or increase steps if you reach the limit.