This paper studies three types of functions arising separately in the
analysis of algorithms that we analyze exactly using similar Mellin transform
techniques. The first is the solution to a Multidimensional Divide-and-Conquer
(MDC) recurrence that arises when solving problems on points in $d$-dimensional
space. The second involves weighted digital sums. Write $n$ in its binary
representation $n=(b_i b_{i-1}... b_1 b_0)_2$ and set $S_M(n) = \sum_{t=0}^i
t^{\bar{M}} b_t 2^t$. We analyze the average $TS_M(n) = \frac{1}{n}\sum_{j<n}
S_M(j)$.