{ "category": "Engineering functions", "display_name": "BESSELY", "entry_kind": "built_in_function", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.BESSELY", "implementation_state": { "answer_bank": { "excel_builds": [ "20527" ], "larger_numeric": 0, "last_bit": 0, "matched": 46, "other_mismatch": 0, "refused": 0, "rows": 46, "unread": 0, "worst_ulp": 0 }, "detail": "Of 258 recorded answers (46 in the answer bank and 212 workbook cells), 2 do not match: 1 differ by more than 16 ULP, 1 differ by at most 16 ULP.", "dnacalc_commit": "9e1884369a678158dd82d3d74188daf986995e87", "in_catalogue": true, "state": "differs", "state_label": "Known larger differences", "summary": "Known larger differences on 2 of 258 recorded answers", "workbook_corpus": { "cells": 212, "larger_numeric": 1, "last_bit": 1, "matched": 210, "worst_ulp": 1 } }, "implementations": [ { "commit": "9e1884369a678158dd82d3d74188daf986995e87", "flavour": "excel-compatibility-candidate", "language": "Rust", "name": "CalcFunc", "own_code": [ "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/engineering.rs#L263-L263", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/bessel.rs#L198-L209", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/bessel.rs#L210-L221", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/bessel.rs#L322-L335", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/bessel_rational.rs#L114-L118", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/bessel_rational.rs#L120-L124", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/bessel_rational.rs#L181-L192", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/bessel_rational.rs#L252-L262" ], "repository": "https://github.com/DnaCalc/DnaCalc", "shared_code": [ "catalogue/engineering::radix_kind", "catalogue/engineering::bessel", "ported/bessel::abs", "ported/bessel::admit_phase", "ported/bessel::order", "ported/bessel::forward", "ported/bessel::finish", "ported/bessel_rational::polynomial", "ported/bessel_rational::polynomial_with", "ported/bessel_rational::j0", "ported/bessel_rational::j1", "ported/excel_numeric::sin_with", "ported/excel_numeric::cos_with", "ported/excel_numeric::excel_sin", "ported/excel_numeric::excel_cos", "ported/excel_numeric/soft87::pack_raw", "ported/excel_numeric/soft87::zero", "ported/excel_numeric/soft87::inf", "ported/excel_numeric/soft87::pack", "ported/excel_numeric/soft87::ext_pi", "ported/excel_numeric/soft87::ext_one", "ported/excel_numeric/soft87::ext_abs", "ported/excel_numeric/soft87::ext_chs" ], "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/engineering.rs#L263-L263", "state": "differs", "suite": null, "summary": "Known larger differences on 2 of 258 recorded answers" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.BESSELY.json", "name": "BESSELY", "notes": [], "schema": "efh.function-reference/v1", "section_order": [ "what-it-does", "try-it", "quirks", "how-to-implement", "version-differences", "alternatives" ], "sections": { "alternatives": "\n[BESSELI](FUNC.BESSELI.md) and [BESSELK](FUNC.BESSELK.md) are modified Bessel functions. [BESSELJ](FUNC.BESSELJ.md) supplies the other ordinary kind.\n\n\n", "how-to-implement": "\nValidate x and the order before selecting a numerical route. Use order-zero and order-one seed approximations. For higher orders the recurrence is `C_(j+1)=(2*j/x)*C_j-C_(j-1)`. The current code runs forward from its Y0 and Y1 seeds. For example the recurrence gives `C2=(2/x)*C1-C0`; its numbers depend on both seed values. Seed coefficients, phase grouping and flushing are separate compatibility questions, with residual differences still recorded. This is a published-method implementation outline, not a claim that every Excel stage is solved.\n\n\n", "quirks": "\nNonnumeric arguments give `#VALUE!`; a negative order gives `#NUM!`. The current real-valued kernel requires positive x. Recorded code also limits truncated order to 10,000,000 and applies phase-based large-argument admission. Published approximation methods remain distinct from an identification of Excel’s numerical body.\n\n\n", "sources": "\n- [Licensed seed and backward helpers](https://github.com/DnaCalc/DnaCalc/blob/da3ecc4fb19a3a5529708c311d0e8f05688ac165/crates/calc-func/src/ported/bessel_rational.rs).\n- [Microsoft: BESSELY function](https://support.microsoft.com/en-us/excel/functions/bessely-function), opened 6 November 2026; syntax, documented argument rules and errors.\n- [DnaCalc implementation](https://github.com/DnaCalc/DnaCalc/blob/da3ecc4fb19a3a5529708c311d0e8f05688ac165/crates/calc-func/src/ported/bessel.rs); implementation steps and the limits identified in the text.\n\n", "try-it": "\n`=BESSELY(2,0)` evaluates the order-zero function at two. The mathematical value is about `0.51037567`; `=BESSELY(0,0)` is outside the current positive-x domain and gives `#NUM!`.\n\n\n", "version-differences": "\nNo same-input comparison between named Excel builds is recorded for this function here. The documented behaviour below is not a measurement of every Excel release.\n\n\n", "what-it-does": "\n`BESSELY(x,n)` evaluates the order-n Bessel function of the second kind. It is a special function used in radial and oscillatory problems, rather than an elementary trigonometric function. The order is truncated to an integer.\n\n\n" }, "signature": { "display": "BESSELY(x, n)", "parameters": [ { "description": null, "name": "x", "optional": false, "repeats": false }, { "description": null, "name": "n", "optional": false, "repeats": false } ], "trailing_repeats": false }, "sources": { "metadata": { "admission": { "label": "implemented", "reason": null }, "arity": { "max": 2, "min": 2 }, "category": "Engineering functions", "classification": { "arg_preparation_profile": "ValuesOnlyPreAdapter", "coercion_lift_profile": "Custom", "determinism_class": "Deterministic", "error_collapse_profile": "None", "fec_dependency_profile": "None", "host_interaction_class": "None", "kernel_signature_class": "Custom", "rich_value_usage": "RichBlind", "surface_fec_dependency_profile": "None", "thread_safety_class": "SafePure", "volatility_class": "NonVolatile" }, "descriptions": { "long": null, "short": "Bessel function of the second kind, Y_n(x)", "short_source": "dna-calc-own" }, "docs": { "english_description": "Returns the Bessel function Yn(x)", "microsoft_url": "https://support.microsoft.com/en-us/office/bessely-function-f3a356b3-da89-42c3-8974-2da54d6353a2" }, "entry_kind": "built_in_function", "localized_family_names": null, "localized_names": [ { "locale": "ar-SA", "name": "BESSELY" }, { "locale": "bg-BG", "name": "BESSELY" }, { "locale": "cs-CZ", "name": "BESSELY" }, { "locale": "da-DK", "name": "BESSELY" }, { "locale": "de-DE", "name": "BESSELY" }, { "locale": "el-GR", "name": "BESSELY" }, { "locale": "en-AU", "name": "BESSELY" }, { "locale": "en-GB", "name": "BESSELY" }, { "locale": "en-US", "name": "BESSELY" }, { "locale": "es-ES", "name": "BESSELY" }, { "locale": "et-EE", "name": "BESSELY" }, { "locale": "fi-FI", "name": "BESSELY" }, { "locale": "fr-FR", "name": "BESSELY*" }, { "locale": "he-IL", "name": "BESSELY" }, { "locale": "hr-HR", "name": "BESSELY" }, { "locale": "hu-HU", "name": "BESSELY" }, { "locale": "id-ID", "name": "BESSELY" }, { "locale": "it-IT", "name": "BESSELY" }, { "locale": "ja-JP", "name": "BESSELY" }, { "locale": "ko-KR", "name": "BESSELY" }, { "locale": "lt-LT", "name": "BESSELY" }, { "locale": "lv-LV", "name": "BESSELY" }, { "locale": "nb-NO", "name": "BESSELY" }, { "locale": "nl-NL", "name": "BESSELY" }, { "locale": "pl-PL", "name": "BESSEL.Y" }, { "locale": "pt-BR", "name": "BESSELY" }, { "locale": "pt-PT", "name": "BESSELY" }, { "locale": "ro-RO", "name": "BESSELY" }, { "locale": "ru-RU", "name": "БЕССЕЛЬ.Y" }, { "locale": "sk-SK", "name": "BESSELY" }, { "locale": "sl-SI", "name": "BESSELY" }, { "locale": "sr-Latn-RS", "name": "BESSELY" }, { "locale": "sv-SE", "name": "BESSELY" }, { "locale": "th-TH", "name": "BESSELY" }, { "locale": "tr-TR", "name": "BESSELY işlevi" }, { "locale": "uk-UA", "name": "BESSELY" }, { "locale": "vi-VN", "name": "BESSELY" }, { "locale": "zh-CN", "name": "BESSELY" }, { "locale": "zh-HK", "name": "BESSELY" }, { "locale": "zh-TW", "name": "BESSELY" } ], "signature": { "display": "BESSELY(x, n)", "parameters": [ { "description": null, "name": "x", "optional": false, "repeats": false }, { "description": null, "name": "n", "optional": false, "repeats": false } ], "trailing_repeats": false }, "surface_name": "BESSELY", "version_marker": null, "xlcall": { "code": "427", "symbol": "xlfBessely" } }, "microsoft": "https://support.microsoft.com/en-us/office/bessely-function-f3a356b3-da89-42c3-8974-2da54d6353a2" }, "try_it": { "formula": "=BESSELY(2,0)" }, "url": "https://handbook.dnacalc.com/functions/BESSELY.html", "variants": [], "versions": [] }