SECH Function (OpenOffice Calc)

• Introduced: First release not established; presence is verified in Apache OpenOffice 4.1.16. Earlier support has not been established here.
• Supported in: Apache OpenOffice 4.1.16; this identifies a verified release, not a final supported version.
• Scope: Desktop Calc, English function names and semicolon-separated formulas.
• Checked: October 14, 2026. Eight reference formulas and the listed diagnostics were recalculated from generated native ODF in 4.1.16 on Linux x86-64, Build 9816. Source and independent reference calculations were also checked.

SECH calculates hyperbolic secant, mathematically 1/cosh(x). It returns a real numeric value for a valid finite input where the defining denominator is nonzero. The implementation evaluates the reciprocal directly, so denominator zeros and floating-point behavior matter. Release entry.

=SECH(Number)

Supply one numeric argument. The argument is a real, dimensionless input; this hyperbolic function has no intrinsic degree unit. The observed TRUE argument becomes 1, and a referenced empty cell becomes 0. Non-numeric text and an extra argument produce errors in the tested cases.

The native column records the saved 4.1.16 results. The independent values use high-precision mathematics; displayed decimals are rounded to twelve places. Integer results remain exact in these small cases.

SECH is a positive, symmetric hyperbolic profile. If t is in A2 and a positive scale τ is in B2, =SECH(A2/B2) describes the profile at the dimensionless ratio t/τ. Its central value is 1 at t=0; the tested ratio 0.5 gives about 0.88681888397. This is a model shape, not automatically a normalized probability density.

SECH(x)×COSH(x)=1, and SECH(x)^2+TANH(x)^2=1 for real x. It is even, so negating x does not change the result. For finite real inputs its mathematical range is above zero and at most 1. The function tends toward zero as |x| grows.

Unlike CSCH, SECH has no real zero-argument pole: SECH(0)=1. It is not an inverse hyperbolic function and does not recover an argument from a cosh value. The finite examples do not establish underflow or intermediate-overflow behavior at extreme arguments.

These additional formulas were recalculated from the same generated ODF input. H5 is a deliberately empty cell where referenced. Error displays are retained as errors, even when an ODS numeric attribute stores zero.

SINH, COSH, TANH.

• Function-specific release entry

The generated ODF input produced the informational load warning “Not all attributes could be read.” After it was acknowledged, the sheet was hard-recalculated and saved separately. Every formula identity, input label and tested result was reconciled, including repeated spaces represented with ODF text elements. This does not certify every style attribute. The separately prepared XLSX input was not executed. A deliberately stale SUM cache changed from 999999 to 3, and an uncached SUM returned 7 after hard recalculation. Native evidence covers the eight reference formulas and listed diagnostics only. Other explanatory compositions are independent mathematical checks; other releases, locales and extreme-value behavior were not established by this run.