Problems 9

Theory.
1. What is the declaration of the gsl_function structure?
2. What is the declaration of the gsl_integration_qag function?
3. What is the declaration of the gsl_integration_qags function?
4. What is the declaration of the gsl_integration_cquad function?
Practice.
1. Numerical integration with Gauss-Kronrod algorithm.
  1. Look up the definition of the error functions erf in Wikipedia.
  2. Implement a function with the signature
    double myerf(double x)
    that calculates the error function erf by direct numerical integration.
    - when x<0 use erf(x)=-erf(-x)
    - When x<1 use the expression
```
erf(x) = (2/√π)∫_₀^{^x} e^-t²
```
      and employ gsl_integration_qags.
    - otherwise use the expression
```
erf(x) = 1 - (2/√π)∫_{_x}^{^∞} e^-t²
```
      and employ gsl_integration_qagiu.
  3. Make a plot where you compare you function with the gsl_sf_erf function from gsl_sf_erf.h .