IMCSCH Function in ONLYOFFICE Spreadsheet Editor: Complex Hyperbolic Cosecant, Syntax and Examples

Use IMCSCH for reciprocal hyperbolic models, odd-function checks, and complex-domain engineering formulas. The input is a complex value z = a + bi (or a+bj as documented). Both a and b are real coefficients; i and j are imaginary-unit suffixes, not separate function arguments. A value such as 1+1i is one input. The mathematical operation is distinct from similarly named ordinary real functions and from circular versus hyperbolic trigonometry.

The exact purpose and function family are stated in the ONLYOFFICE IMCSCH help page; the worked values below were calculated independently using standard complex mathematics, not copied from screenshots. Input data and expected outputs are deliberately simple enough to reproduce and audit.

=IMCSCH(inumber)

There are no documented optional arguments and no second parameter. =IMCSCH(D2) is therefore structurally different from =IMCSCH(B2,C2), which does not follow this function’s documented syntax. Enter a text literal with quotes when appropriate (=IMCSCH("1+1i")) or construct the input with the separate documented COMPLEX function (=IMCSCH(COMPLEX(1,1))). The latter’s formal syntax is COMPLEX(real_num, i_num, [suffix]); its optional suffix accepts i or j and defaults to i. See COMPLEX.

Formula-language note: The English ONLYOFFICE Insert functions guide documents formula entry beginning with = and comma-separated multiple arguments. =IMCSCH(D2) has only one argument and requires no internal separator. Localized formula names and argument separators can vary with settings; this guide has not validated translated names or locale-specific entry. Do not convert an English help example into an unverified locale guarantee.

1. Open a new, empty worksheet in an available ONLYOFFICE Spreadsheet Editor. Keep calculation mode at its usual automatic setting or use Formula → Calculation to recalculate if required; this menu exists in the current Docs guide.
2. In A1:I1 enter: Case, Real, Imaginary, Complex input, IMCSCH output, Expected real, Expected imaginary, Observed real, Observed imaginary.
3. Copy the input label and the two numeric coefficient columns into A2:C12; the row-number column is a guide, not data. For D2 enter =COMPLEX(B2,C2); fill the formula down through D12. COMPLEX is separately documented by ONLYOFFICE.
4. In E2 enter =IMCSCH(D2); fill through E12. In F2:G12, type the six-decimal independently computed expected coefficients from the final two table columns.
5. In H2 enter =IMREAL(E2) and in I2 enter =IMAGINARY(E2); fill both down through row 12. These two vendor functions extract the real and imaginary coefficients. Compare H with F and I with G numerically, rather than relying on the formatting of the complex result in E.
6. Where your locale supports the English syntax shown, add J1 = Within tolerance? and J2 = =AND(ABS(H2-F2)<0.00001,ABS(I2-G2)<0.00001) and fill down. This is a proposed test formula, not a reported native execution. Inputs may produce slightly different displayed precision without being mathematically wrong.

Expected output interpretation: These are numeric components of a mathematical complex value. Actual formatting of the result in column E may use i or j, omit zero coefficients, or show a different number of decimals; none of those display choices was observed in a native test. Use the extracted coefficients and a numeric tolerance to evaluate the formula. The table contains 11 independently cross-checked inputs. Floating-point tolerances prevent false failure from normal rounding.

Two copy-paste shortcuts

=IMCSCH(COMPLEX(1,1))
=IMCSCH(COMPLEX(1,-1))

The independently calculated complex outputs of those two formulas are respectively 0.303931 − 0.621518i and 0.303931 + 0.621518i. They are mathematical expected results to approximately six decimals, not the text of a verified ONLYOFFICE cell. Enter as formulas and use IMREAL / IMAGINARY to verify numerically.

The mathematical definition is csch(z) = 1/sinh(z). Also, csch(-z) = -csch(z). These are derived complex-analysis identities, not independently documented ONLYOFFICE-specific runtime quirks. You can compare the results of two different worksheet paths in the following controlled way.

Alternative formula for D2:

=IMDIV(COMPLEX(1,0),IMSINH(D2))

Mathematically equivalent if sinh(z) is nonzero. The related ONLYOFFICE function pages are IMCOS, IMSIN, IMCOSH, IMSINH, IMDIV, and COMPLEX.

Symmetry test: Put =COMPLEX(-B2,-C2) in K2, then =IMCSCH(K2) in L2; compare its extracted numeric coefficients against the original output in E2. The relation to test is csch(-z) = -csch(z). A sign change applies to both real and imaginary coefficients when the function is odd. Fill down only over nonsingular inputs. In independent math validation, this identity passed across all 11 listed non-pole inputs.

Component equation (for derivation and debugging): csch(z) = 1 / [sinh(a)cos(b) + i·cosh(a)sin(b)] for z=a+bi, provided the denominator is not zero. This relation helps explain why a real-only spreadsheet function cannot generally substitute for a complex one. Unlike the vendor syntax, this is mathematical explanation, with original examples independently cross-checked.

Special-angle or zero control: For z=iθ, csch(z)=−i/sin(θ) if sin(θ) is nonzero. At z=0, IMCSCH has no finite mathematical value. The exact native ONLYOFFICE error code/string for the input = IMCSCH(COMPLEX(0,0)) (without the space after = in actual entry) has not been tested; do not print a made-up result.

Compare IMCSCH to an independent worksheet expression using IMDIV and IMSINH, and treat mathematical singularities as exceptions rather than expected text errors. To use the worksheet as a controlled model, keep input coefficients in B2:C12, build complex values in D, and compute the target function in E. Use separate cells for parameter assumptions and units: the imaginary coefficient is not a unit conversion or an implied angle. Most phase-related trig identities assume radians; the current function reference does not offer a degrees parameter.

For a parameter sweep, replace the sample input coefficients with a domain-specific set while retaining the coefficient-extraction and tolerance checks. Mark rows close to mathematical singularities for review instead of interpreting very large values as automatically erroneous. Keep the raw formulas visible for an auditor—do not replace live formulas with screenshots.

Additional mathematical boundary: If the output is extremely large near zero, check the reciprocal relationship and how many digits the upstream complex argument actually contains. No official function page reviewed here specifies a complete cross-platform native-error matrix, maximum exact input length, or exact string formatting for these examples. Documented purpose/syntax must not be expanded into undocumented test outcomes.

The dated source of the function name, operation and argument is the current unversioned ONLYOFFICE Docs help reference, checked 2026-10-13 (UTC). The current Insert functions catalogue lists IMCSCH in the Engineering family. This supports a documentation-availability claim, not a first-shipped-version claim for each client. Docs web editors and Desktop Editors are separate application distributions; a Docs help page does not independently verify the exact native behaviour of a historical desktop release, mobile app or older self-hosted deployment.

If working in a versioned environment, record the app type (web/desktop), precise version/build, operating system, selected interface/formula language, regional settings and whether the workbook is .xlsx or another format. Only then compare the formulas and extracted coefficients, including special values. Consult ONLYOFFICE Desktop release history separately instead of borrowing another spreadsheet application’s compatibility notes. The Advanced Settings guide documents regional/language options; a locale-specific translated function name has not been established by this research.

Compatibility status for this manuscript: English unversioned vendor syntax and current Docs catalogue DOCUMENTATION_CONFIRMED; mathematical examples INDEPENDENT_CALCULATION_CONFIRMED; ONLYOFFICE Docs web execution NOT_TESTED; Desktop Editors native execution NOT_TESTED; earliest supported versions and exact error strings NOT_VERIFIED.

• IMCSCH: current ONLYOFFICE help (required argument and purpose).
• ONLYOFFICE Spreadsheet Editor: Insert functions, formula entry, recalculation and Engineering index.
• COMPLEX: compose one value from real and imaginary coefficients.
• IMREAL: extract the real coefficient and IMAGINARY: extract the imaginary coefficient.
• IMDIV: complex division.
• ONLYOFFICE Spreadsheet Editor: Advanced Settings.
• ONLYOFFICE Desktop Editors: release history.