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6 Exponential, Logarithmic, Sine, and Cosine IntegralsProperties

§6.15 Sums

6.15.1 n=1Ci(πn) =12(ln2-γ),
6.15.2 n=1si(πn)n =12π(lnπ-1),
6.15.3 n=1(-1)nCi(2πn) =1-ln2-12γ,
6.15.4 n=1(-1)nsi(2πn)n =π(32ln2-1).

For further sums see Fempl (1960), Hansen (1975, pp. 423–424), Harris (2000), Prudnikov et al. (1986b, vol. 2, pp. 649–650), and Slavić (1974).