RE: References for Numerical Integration

[Jacques Gélinas <jacquesg00@hotmail.com>]

> Any other references would also be appreciated. Kevin

1. The example intnum(x=0,oo, (sin(x)^4)/(x)^2) is a Fourier Sine Transform of an oscillating function,
sin^3(x)/x^2. It could be possible to get an infinite series for it with oscillating and decreasing terms,
and then perhaps use Euler acceleration ?

2. Philip Davis+Philip Rabinowitz,, Methods of numerical integration (1984, p. 240)
show how evaluate the Fourier Sine Transform of sin^2(x/2)/x i.e.

                     intnum(x=0,oo, sin(x/2)^2/x sin(wx) )

for w=1 (Pi/8), w=10 (0), interpolating by subintervals and integrating the resulting formulas
to get 4 correct digits.

3. Piessens+al, Quadpack. A subroutine package for automatic integration, Springer, 1983.
Subroutine QAWFE (adaptative) http://www.netlib.org/quadpack/index.html

Hope this helps,

Jacques Gélinas