Compute an enclosure of the definite integral $$\int_{a}^{b} f(z) \text{d}z$$ taking as the path of integration the line segment from \(a\) to \(b\).
arb_integrate(func, a, b, param = NULL, rtol = NULL, atol = NULL,
control = NULL, prec = flintPrec())
acb_integrate(func, a, b, param = NULL, rtol = NULL, atol = NULL,
control = NULL, prec = flintPrec())An arb or acb vector of
length 1 giving an enclosure of the definite integral.
a function of the form function (z, param, order, prec)
specifying the integrand. Unused trailing arguments can omitted.
real or complex numbers or enclosures indicating finite limits of integration.
an R object typically specifying parameters of the integrand,
passed to func.
a positive real number less than 1 that the relative error in any
subinterval should not exceed. 2^-prec by default.
a positive real number that the absolute error in any subinterval
should not exceed. The value 0 indicates that convergence should
account only for relative error. 2^-prec by default.
a named list of options for integration.
a positive integer indicating the working precision as a number of
bits, passed to func.
func(z, param, order, prec) computes an enclosure for the
integrand on z, where z is (and the return value of
func must be) an arb or
acb vector of length 1. If the integer
order is nonzero, then func must give a nonfinite result
if the integrand is not holomorphic on z, in particular if the
integrand composes functions that are bounded on z with branch
cuts whose intersection with z is nonempty.
The list control admits components deg.limit,
eval.limit, depth.limit, use.heap, and
verbose. These correspond to so-named members of the
C struct acb_calc_integrate_opt_struct; see the
FLINT documentation for details.
The FLINT documentation of the underlying C function: https://flintlib.org/doc/arb_calc.html
Classes arb and acb;
function integrate in base.