Abstract
The function [(x – t1)″1 (x – t2)″2 … (x – tN)″N]−1 with N, [Formula: see text], is explicitly expanded in partial fractions. A general recursion relation is also derived. Of particular interest are the cases N = 2 and N = 3. For N = 2, three partial-fraction expansions are compared and a "symmetrical" expansion is shown to be the most useful for evaluating various finite-limit and infinite-limit principal-value integrals. Such expressions are prototypes of integrals containing products of Green's functions, which are presently being studied in intermediate-energy nuclear physics. Also, a complex-contour evaluation provides another derivation of the symmetrical partial-fraction expansions.
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