SERIESSUM in Calligra Sheets: Evaluate a Finite Power Series

=SERIESSUM(x; n; m; coefficients)

Use all four arguments. x is the base, n the first exponent, m the increment between exponents, and coefficients a one-dimensional numeric range or one numeric coefficient. With coefficients a₀ through aₖ, the result is the sum of aᵢ×x^(n+i×m).

The order of the coefficient cells matters. A vertical range is the clearest reproducible layout. n and m are converted to floating values, so they need not be integers; for fractional exponents keep x positive to avoid real-domain ambiguity. There are no useful omitted defaults.

Source safety caution: registration permits three arguments, but the implementation accesses the fourth. Do not call the three-argument form. Extra arguments are not additional coefficients: only the fourth argument is read as the coefficient collection. Neither behavior should be used as a shortcut for the documented four-argument syntax.

Use a dimensionless normalized sensor input x and a model y = 1 + 2x + 3x², where y is in calibrated output units.

1. Enter 1, 2, 3 in H15, H16, H17.
2. Enter 2 in A2 for the normalized input.
3. In B2 enter =SERIESSUM(A2;0;1;H15:H17).
4. The expected result is 17 output units.
5. In C2 check the same calculation with =H15+H16*A2+H17*A2^2.

If x has physical units rather than being normalized, the coefficients generally need different units so that every term has the same final unit. A spreadsheet will add inconsistent terms without knowing that the model is dimensionally wrong.

For x + 2x³ + 3x⁵, keep the coefficients and enter =SERIESSUM(2;1;2;H15:H17). The reference value is 114, from 2 + 16 + 96. The exponent step is 2, so this is not the quadratic model above.

For √x + 2x + 3x^(3/2), use =SERIESSUM(4;0.5;0.5;H15:H17). The result is 34, from 2 + 8 + 24. These finite evaluations say nothing about convergence of an associated infinite series or truncation error. If the coefficients approximate a function, assess the approximation interval and omitted terms separately.

The inspected implementation returns a numeric error when x = 0 and n = 0. That affects even an ordinary polynomial with a constant term: the mathematical polynomial value at zero would be its first coefficient, but this implementation rejects the call. Evaluate the known constant term separately when that boundary is required.

For x = 0 and n ≠ 0, the implementation skips its loop and returns zero. This agrees with positive exponents but can conceal a negative-exponent singularity. Restrict zero inputs to models where all relevant exponents are positive; do not treat a returned zero as validation of reciprocal powers at zero.

When m = 0 and x is nonzero, every term has the same exponent. With the example coefficients, =SERIESSUM(2;0;0;H15:H17) gives 6. A scalar coefficient is also possible: =SERIESSUM(2;0;1;3) is 3.

Keep coefficients genuinely numeric. The implementation reads coefficient elements directly as floating values rather than establishing a general text/error propagation contract. Large powers, cancellation between terms and accumulated rounding can reduce numerical reliability; no universal precision bound is implied.

POWER and SUM can express individual terms and their total. A spreadsheet with a similarly named SERIESSUM may handle zero and invalid arity differently. Preserve coefficient order and test the x=0 boundary when exchanging a polynomial workbook.

Reviewed October 18, 2026. The relevant implementation file and shared numerical/conversion files were compared between official 25.04.2 and 26.08.2 source and are byte-identical. This establishes source equivalence for the inspected code, not identical behavior on every platform or a native test of 26.08.2. The earliest release containing SERIESSUM has not been established; these version numbers are not introduction dates.

Mathematical reference values above were calculated independently. The native results below were obtained in Calligra Sheets 25.04.2 on Linux, October 18, 2026; no native 26.08.2 execution is claimed. No unstated locale, import or array-entry behavior is implied.

• KDE 26.08.2 implementation.
• KDE 25.04.2 implementation.
• KDE shared numerical implementation.
• KDE function handbook: SERIESSUM.

These formulas were recalculated in the actual application and read back from its completed native-saved workbook. The image is an unmodified application screenshot. The earlier mathematical calculations remain independent references; this table records actual saved results.

Native H15:H17 contains coefficients 1,2,3. Every call has all four arguments; the unsafe missing-coefficient form was not executed.

Display formatting may show fewer digits than the saved value. The tested cases do not establish every coercion, extreme magnitude or cross-application import behavior.