Can you please direct me towards the reference paper that describes the quadrature method that was used in the "integrate1d" function in Gauss?
Also, any details regarding the type of quadrature (e.g.,Gaussian) and how the nodes and their relative weights are determined would be very helpful.
The algorithm in
integrate1d is very similar to what is in the QUADPACK functions QAGS and QAGI. For finite intervals,
integrate1d uses a 21 point adaptive Gauss-Kronrod quadrature. Infinite intervals are mapped to (0,1] and then use a 15 point adaptive Gauss-Kronrod quadrature.