By putting this expression, as well as appropriate expressions for Si (a) and 84(a) (from Equation 27), into Equation 44, the following is obtained: SgoodC*5) can be found by using Equation 54, and letting "a" approach co. To do this, recall that, from Equations 28a and 28b (based on Reference 11, page 177), for large "a", Jn(a) is bounded by l/^a for all n. Thus, Jn(a) approaches 0 as "a” approaches co. This is true even if Jn(a) is divided by a positive power of "a" and/or raised to a positive power. Therefore, all of the terms containing "a" in Equation 54 are zero for a = co, so that Sgood(°°) = 74/7. By combining this result with Equation 41, it is seen that the fraction of energy contained within non-dimensionalized radius "a" for the "good" case is given by:
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