Description
Return a logarithmic-derivative residue from zero/pole orders.
Differential-calculus formulas relate supplied local values and derivatives under explicit coordinate and unit conventions. A tangent term, curvature expression or directional derivative assumes the required differentiability and regularity; substituting numerical derivatives does not verify those hypotheses for an actual function.
Return a logarithmic-derivative residue from zero/pole orders.
When to use this tool
Use Logarithmic Derivative Residue Term when evaluating the stated local differential-calculus identity from supplied values.
How to use the tool and how it works
- Enter multiplicity, poleOrder. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read residue. Use the output convention below.
Return a logarithmic-derivative residue from zero/pole orders. Require nonnegative whole multiplicity/poleOrder; residue = multiplicity-poleOrder.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| multiplicity | Multiplicity | Required. Safe integer; minimum 0. |
| poleOrder | Pole Order | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| residue | Residue | Required. Safe integer. |
{
"input": {
"multiplicity": 3,
"poleOrder": 1
},
"output": {
"residue": 2
}
}Limitations and assumptions
- The orders are asserted for a meromorphic local model; no complex function, cancellation or singularity is analyzed.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- 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. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Differentiate or validate the complete function and its domain first; use suitable symbolic or numerical methods and check regularity and coordinate conventions for the intended interpretation.
References
Similar or alternative tools
- Logarithmic Time Derivative Factor
Convert a time derivative to a natural-log-time derivative.
- Local Logarithmic Second Derivative
Return the local second logarithmic derivative.