1608	 Numerical Integration of Function That Has a Pole	 It is common to need to integrate numerically functions that diverge somewhere outside the range of integration. Even if the divergence occurs quite far away integration formulas like Simpson s that depend on fitting a polynomial usually will be inaccurate near a pole they will be very bad. A method is described that gives formulas that will integrate functions of this kind accurately if the orders and positions of the poles are known. Explicit formulas are given that are easy to use on an automatic computer. It is shown that they can be used for some other singularities as well as poles. If the integral converges integration can be carried to the singularity. The accuracy of the integration with a pole of second order is discussed and as an example the new formula is compared with Simpson s. The new formulas are useful even far from the pole while near the pole their advantage is overwhelming.
