Description
Check local power integrability near a finite endpoint.
Integration depends on the domain, orientation, coordinate change and endpoint behavior. A boundary contribution, Jacobian factor or power-tail test is a local part of an integral calculation; convergence, a valid change of variables and the complete integral require their own hypotheses.
Check local power integrability near a finite endpoint.
When to use this tool
Use Endpoint Singularity Integrability Power when evaluating the stated integral contribution, orientation, Jacobian or convergence condition.
How to use the tool and how it works
- Enter power. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read integrable, logarithmicBoundary. Inspect integrable, logarithmicBoundary before interpreting the associated values.
Check local power integrability near a finite endpoint. integrable means power > -1, logarithmicBoundary means power === -1.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| power | Power | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| integrable | Integrable | Required. Boolean. |
| logarithmicBoundary | Logarithmic Boundary | Required. Boolean. |
{
"input": {
"power": -0.5
},
"output": {
"integrable": true,
"logarithmicBoundary": false
}
}Limitations and assumptions
- This assumes a nonzero constant times positive distance-to-endpoint raised to power; tails and additional singular factors are not 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
Specify and analyze the complete integrand and domain, including endpoint singularities, coordinate invertibility and any omitted boundary or interior terms.
References
Similar or alternative tools
- Improper Tail Power Integrability
Check power-tail integrability at infinity.
- Endpoint Trapezoid Correction Term
Compute the explicit endpoint trapezoid correction relative to a left rectangle on an oriented interval.