IMCSCH Function (OpenOffice Calc)

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

IMCSCH returns the reciprocal of complex hyperbolic sine where the denominator is nonzero. The name refers to hyperbolic cosecant; it is not an inverse hyperbolic function. For z=a+bi, the independent component formula is csch(a+bi)=[2 sinh(a)cos(b)−2i cosh(a)sin(b)]/[cosh(2a)−cos(2b)]. Release entry.

=IMCSCH(ComplexNumber)

Exactly one complex-number argument is required. The add-in parses pure real forms and complex strings with lowercase i or j. Its strict parser rejects nonempty malformed text and empty strings. The trigonometric angles in the component formulas are in radians, not degrees.

The native column records the saved 4.1.16 results. The native strings are retained exactly. Independent component references are rounded to twelve decimal places, with rounded negative zero shown as zero. A tiny stored residual can therefore appear in the native string beside a reference component rounded to zero. Every successful result below is string-typed, including pure real-looking outputs.

For 1+i the components are approximately 0.303931001628 and −0.621518017170. For a real input 1 the result is the positive real value 1/sinh(1). For i alone it is −i/sin(1), showing that swapping real and imaginary inputs changes which ordinary or hyperbolic function appears.

For a worksheet, place a validated complex value in A2 and use =IMCSCH(A2). This is an illustrative layout for the tested literal argument. Keeping real and imaginary measurements separately can make unit, sign and parsing mistakes easier to detect.

Hyperbolic cosecant is odd and respects conjugation. Where defined, csch(z)sinh(z)=1. Its relationship to ordinary cosecant can be written csch(z)=i csc(iz). This follows from sin(iz)=i sinh(z), including the sign from dividing by i.

For real large positive inputs, the mathematical value approaches zero. An implementation that explicitly forms large hyperbolic intermediates can still face overflow or cancellation before reaching a small final answer. The ordinary cases do not certify every extreme branch.

Zero is a pole and the native call returns an error. More generally the mathematical poles occur at z=kπi for integer k. A stored decimal angle near such a pole is not exact mathematical π. Keep input-approximation effects separate from the strict invalid-text and wrong-arity diagnostics.

These additional formulas were recalculated through the same generated-ODF path. Error displays are retained as errors, even when an ODS numeric attribute stores zero.

The IMCSCH guide for LibreOffice Calc documents that product’s own syntax and tested behavior. A shared function name does not guarantee the same argument conversion, text parsing, branch or precision rules.

• Function-specific release entry
• Complex algorithm or collection helper
• Strict complex-string parser
• Finite-output string formatter

The saved ODS retained every tested formula identity. A deliberately stale SUM cache changed from 999999 to 3, and an uncached SUM returned 7 after hard recalculation. The application reported “Not all attributes could be read” on loading the generated input. All tested identities and input text survived, but preservation of every style attribute was not established. Native evidence covers the eight reference formulas and listed diagnostics only; it does not establish XLSX-import or manual-entry behavior. Other explanatory compositions are independent mathematical checks; other releases, locales and extreme-value behavior were not established by this run.