| Interface | Description |
|---|---|
| SubstitutionRule |
A substitution rule specifies \(x(t)\) and \(\frac{\mathrm{d} x}{\mathrm{d} t}\).
|
| Class | Description |
|---|---|
| DoubleExponential |
This transformation speeds up the convergence of the Trapezoidal Rule exponentially.
|
| DoubleExponential4HalfRealLine |
This transformation is good for the region \((0, +\infty)\).
|
| DoubleExponential4RealLine |
This transformation is good for the region \((-\infty, +\infty)\).
|
| Exponential |
This transformation is good for when the lower limit is finite, the upper limit is infinite, and the integrand falls off exponentially.
|
| InvertingVariable |
This is the inverting-variable transformation.
|
| MixedRule |
The mixed rule is good for functions that fall off rapidly at infinity, e.g., \(e^{x^2}\) or \(e^x\)
The integral region is \((0, +\infty)\).
|
| NoChangeOfVariable |
This is a dummy substitution rule that does not change any variable.
|
| PowerLawSingularity |
This transformation is good for an integral which diverges at one of the end points.
|
| StandardInterval |
This transformation is for mapping integral region from [a, b] to [-1, 1].
|
| Enum | Description |
|---|---|
| PowerLawSingularity.PowerLawSingularityType |
the type of end point divergence
|