Mathematical Writing by Franco Vivaldi

Author:Franco Vivaldi
Language: eng
Format: epub
Publisher: Springer London, London

(6.5)

The meaning of is not at all evident. This quantity depends on , but its dependence does not appear explicitly; a poor choice of symbols obscures matters further. We note that the parameters are integers, since they are the upper limit of the inner summation; accordingly, we replace the symbol with —see (6.1). Then we adopt the ‘divide and conquer’ method, splitting up the sum as follows:

We now see that is a power series in ; its coefficients are finite sums, determined by the elements of an integer sequence. These are sums of arithmetic progressions, which can be evaluated explicitly:

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