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The evaluation of one family of triple integrals. (English. Russian original) Zbl 0803.65024
Comput. Math. Math. Phys. 32, No. 10, 1487-1489 (1992); translation from Zh. Vychisl. Mat. Mat. Fiz. 32, No. 10, 1658-1660 (1992).
The paper is devoted to the computation of the lattice Green function \(G(l,m,n)\) (the random-walk potential on a body-centered cubic lattice). The authors give new recurrence relations for \(G(l,m,n)\) and present an algorithm for finding the value of \(G(l,m,n)\) at any fixed point in terms of \(G(0,0,0)\). A new simple algorithm for direct calculation of \(G(0,0,0)\) is also constructed.
65D32 Numerical quadrature and cubature formulas
41A55 Approximate quadratures
41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)