& Tornado Alley
The integral of ∫r∞(exp(-z)/z²)dz in important in the physics of atomic nuclei. For convenience define
This function can be evaluated by numerical approximation over an inteval of r to R by dividing the interval into N increments of Δr and using the trapezoidal rule; i.e.,
where Δr=(R-r)/N and ri=r+i*Δr.
The error involved in truncating the integration at R is bounded by exp(-R)/R. Thus if R=10 then the error due to the truncation is less than 4.54×10-6 and if R=15 then the error is less than 2.04×10-8. For R=20 the truncation error is less than 1.03×10-10 In addition to the error from the truncation of the integral there is error from applying the trapezoidal rule to a function that is curved.
Using R=20 and the trapezoidal quadrature method some of the values of w(r) are
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