## Types in MathNet.Numerics

Type DifferIntegrate

Namespace MathNet.Numerics

### Public Static Functions

#### doubleDoubleExponential(Func<double, double> f, double x, double order, double x0, double targetAbsoluteError)

Evaluates the Riemann-Liouville fractional derivative that uses the double exponential integration.

order = 1.0 : normal derivative

order = 0.5 : semi-derivative

order = -0.5 : semi-integral

order = -1.0 : normal integral

##### Parameters
###### `Func<double, double>` f

The analytic smooth function to differintegrate.

###### `double` x

The evaluation point.

###### `double` order

The order of fractional derivative.

###### `double` x0

The reference point of integration.

###### `double` targetAbsoluteError

The expected relative accuracy of the Double-Exponential integration.

##### Return
###### `double`

Approximation of the differintegral of order n at x.

#### doubleGaussKronrod(Func<double, double> f, double x, double order, double x0, double targetRelativeError, int gaussKronrodPoints)

Evaluates the Riemann-Liouville fractional derivative that uses the Gauss-Kronrod integration.

order = 1.0 : normal derivative

order = 0.5 : semi-derivative

order = -0.5 : semi-integral

order = -1.0 : normal integral

##### Parameters
###### `Func<double, double>` f

The analytic smooth function to differintegrate.

###### `double` x

The evaluation point.

###### `double` order

The order of fractional derivative.

###### `double` x0

The reference point of integration.

###### `double` targetRelativeError

The expected relative accuracy of the Gauss-Kronrod integration.

###### `int` gaussKronrodPoints

The number of Gauss-Kronrod points. Pre-computed for 15, 21, 31, 41, 51 and 61 points.

##### Return
###### `double`

Approximation of the differintegral of order n at x.

#### doubleGaussLegendre(Func<double, double> f, double x, double order, double x0, int gaussLegendrePoints)

Evaluates the Riemann-Liouville fractional derivative that uses the Gauss-Legendre integration.

order = 1.0 : normal derivative

order = 0.5 : semi-derivative

order = -0.5 : semi-integral

order = -1.0 : normal integral

##### Parameters
###### `Func<double, double>` f

The analytic smooth function to differintegrate.

###### `double` x

The evaluation point.

###### `double` order

The order of fractional derivative.

###### `double` x0

The reference point of integration.

###### `int` gaussLegendrePoints

The number of Gauss-Legendre points.

##### Return
###### `double`

Approximation of the differintegral of order n at x.