The Watson integral for the d-dimensional hypercubic lattice Wd = 1/pi (d) integral (pi)(0)...integral (pi)(0) d theta (1)...theta (d)/d - (cos theta (1) +...+ cos theta (d)) and the associated logarithmic integral L-d = 1/pi (d) integral (pi)(0)...integral (pi)(0) ln [d - (cos theta (1) +...+ cos theta (d))] d theta (1)...d theta (d) are investigated. In particular, a new method is developed which enables one to calculate the numerical values of {L-d : d = 1, 2, ...} and {W-d : d = 3, 4, ...} with extremely high precision. The asymptotic behaviour of Ld and Wd as d --> infinity is also determined. Finally, some generalizations of the results are briefly discussed. [References: 12]
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