Description
Return contribution=coefficients[index]*impulse for a valid zero-based index.
A sequence rule specifies an index origin, state order, and relation among terms. Advancing one step, mapping an index, and checking a local residual answer different questions. Supplied coefficients or periods define a model; they do not establish that observations follow it.
Return contribution=coefficients[index]*impulse for a valid zero-based index.
When to use this tool
Use Linear Recurrence Coefficient Impulse Term when you need this particular index map, recurrence step, count, or local algebraic term under supplied sequence conventions.
How to use the tool and how it works
- Enter coefficients, index, impulse. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read contribution. Use the output convention below.
Return contribution=coefficients[index]*impulse for a valid zero-based index.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| coefficients | Coefficients | Required. Array of finite number; maximum items 256. |
| index | Zero-based index unless the mechanics explicitly state otherwise. | Required. Safe integer; minimum 0. |
| impulse | Impulse | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| contribution | One term under the stated formula, not necessarily a complete statistic. | Required. Finite number. |
{
"input": {
"coefficients": [
2,
-1
],
"index": 1,
"impulse": 3
},
"output": {
"contribution": -3
}
}Limitations and assumptions
- This is one selected coefficient's impulse term, not a complete response, recurrence evaluation, or dynamically inferred coefficient.
- The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Choose exact integer arithmetic when the index or coefficient range requires it. A complete sequence analysis needs actual terms and a consistent index and state-order convention beyond one local step.
References
Similar or alternative tools
- Sequence: Linear Recurrence First Difference Step
Advance one short real linear recurrence with oldest-to-newest state and matching coefficient order, returning next state and its first difference; no symbolic recurrence solving.
- Recurrence Coefficient Leading Gap
Inspect a supplied leading-to-trailing recurrence coefficient list without solving the recurrence.