intl Cauchy integral along a circular arc

## Syntax

                y = intl(a, b, z0, r, f)
                y = intl(a, b, z0, r, f, abserr)
                y = intl(a, b, z0, r, f, abserr, relerr)

## Arguments

z0
  a complex number

a, b
  two real numbers

r
  positive real number

f
  identifier of the function to be integrated (type 13 or 130).

abserr, relerr
  real scalars: absolute and relative numerical tolerances. Default values are `1.d-13` and `1d-8`.

## Description

If `f` is a complex-valued function, `intl(a,b,z0,r,f)` computes the integral of `f(z)dz` along the curve in the complex plane defined by `z0 + r.*exp(%i*t)` for `a<=t<=b` .(part of the circle with center `z0` and radius `r` with phase between `a` and `b`).

## Examples

    function y = f(z)
      y = z^(3 + %pi * %i)
    endfunction

    intl(1, 2, 1+%i, 3, f)

## See also

- intc
- integrate

## History

2024.0.0 Default `abserr` and `relerr` values standardized: `1d-13` and `1d-8` instead of `%eps` and `1d-12`.