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Abstract

Integrating Eq. ( 13) between -1 and +1 gives another relation between the c< c0(l -In 2)IiQc) -cJoik) = 0 so that, solving for c0 and c, ,and the final solution may now be written down by substituting for h(x) and the c< in Eq. ( 13).The special case of small k is of interest; to the first order,where the first term is the well-known solution of Eq. ( 12) for k = 0.The correction term bears a ratio to the first term of approximately (|fcx), which is of the expected magnitude.To conclude, it may be remarked that to write out a formal solution is estimated to require about 2n3/2 hours of labor for that case in which P and Q are nth order polynomials.Of course, once such a solution has been tabulated, it may be used for a number of kernels or parameters.Note also, as previously mentioned, the possibility of curvefitting.In particular, if a large number of terms are to be used, it may be worthwhile to set P = 1 and represent the kernel behavior by [In \ x -t\ +Q] alone; the Q terms could then of course be absorbed directly into g(x) and Eq. ( 3) used.

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