Collabora Office ERF: Gaussian error integrals over one or two limits

=ERF(LowerLimit [; UpperLimit])

The official ERF help specifies the optional upper limit. Mathematically, the one-argument error function is 2/sqrt(π) times the integral of exp(−t²) from 0 to x. Its inputs are dimensionless coordinates in that expression.

Despite the parameter name LowerLimit, ERF(x) means integration from 0 to x. With two arguments, ERF(a;b)=erf(b)−erf(a). A negative limit is meaningful, and reversed limits produce a signed negative integral. The function does not reorder your bounds.

The exact package source registers ERF in the bundled analysis component. Its getErf evaluator uses the optional argument to choose one value or a difference, and its numeric helper calls the standard mathematical error function. This source mapping establishes the documented contract without claiming an installed application was run.

Enter B2 = 0 and B3 = 1. Compare:

=ERF(B3)
=ERF(B2;B3)

Both independently evaluate to 0.8427007929497149. The equality follows because erf(0)=0. It does not mean that the first argument is always ignored in the two-limit form.

For =ERF(1;2), independently calculated erf(2) is approximately 0.9953222650189527. Subtracting erf(1) gives 0.1526214720692379. The interval result is therefore much smaller than ERF(2), because the area from zero to one has been excluded.

The reference values were independently checked with a high-precision alternating power series for the Gaussian integral, rather than by executing the vendor component. Decimal output shown here is a mathematical reference; it is not a universal promise of displayed digits or runtime accuracy in every build.

The standard-normal CDF satisfies Φ(z)=0.5×(1+erf(z/sqrt(2))). For a symmetric interval from −z to z, its probability is erf(z/sqrt(2)) when z is nonnegative.

Thus =ERF(1/SQRT(2)) independently gives approximately 0.6826894921, the standard-normal model probability between −1 and 1. The division by sqrt(2) is essential: ERF(1) is not the same probability.

For a normal variable with mean μ and positive standard deviation σ, convert an endpoint x to (x−μ)/(σ×sqrt(2)) before using the error-function form. For two endpoints, the corresponding normal interval probability is one half of the difference of their error-function values. The scale and factor of one half arise from the normal density’s normalization, not from an optional ERF mode.

This is a mathematical relationship under a stated model. ERF does not estimate the mean or standard deviation or assess whether observed data are normal.

The two-limit value can exceed 1 because it is a difference of error functions, each ranging between −1 and 1. It is not automatically a probability. A negative value for reversed bounds is likewise a signed integral, not a negative probability assigned to an event.

The inspected add-in checks the final result for finiteness; this guide does not invent a localized error code for every invalid conversion or nonfinite argument. For large close positive limits, subtracting two values near 1 can lose relative precision. A small finite control cannot certify accurate extreme-tail interval differences.

ERF.PRECISE has a one-limit contract. ERF additionally supports an upper limit and performs the difference described above. Do not collapse the two names into a single signature or infer identical cross-platform availability from the shared mathematical function. The presence of “PRECISE” in another name is not a measured accuracy comparison for these builds.

This guide covers the new Collabora Office desktop for Linux, using the Flathub source tag coda-26.04.4.3-1 and commit 81339d176148d0d5c81ff05d82540f58f8aaa117. The official desktop release notes and Linux package manifest identify that product/build. The package manifest is a dated observation from October 18, 2026, rather than an installed-binary check.

The 26.04 function help and exact evaluator source were inspected on October 18, 2026. Expected examples were independently calculated; no Collabora application was run. Expected scalar results were derived from the documented contracts, inspected source and independent calculations; native output formatting and error localization have not been tested. Classic, Online/CODE, other operating systems and file-format round trips require their own checks.

Availability here is established from the function-specific help and the mapped package source. Related functions may have different arguments or boundary rules. The first Collabora release introducing this function is not established by the reviewed sources. No cited retirement or deprecation notice was found. Unknown introduction dates do not imply that the function is deprecated. File-format round trips require separate verification.

• ERF.PRECISE: compare the one-limit signature
• NORM.S.DIST: evaluate standard-normal probability with its own mode argument