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We use dimensional regularization to calculate the ${\cal O}(\ep^2)$expansion of all scalar one-loop one-, two-, three- and four-point integralsthat are needed in the calculation of hadronic heavy quark production. TheLaurent series up to ${\cal O}(\ep^2)$ is needed as input to that part of theNNLO corrections to heavy flavor production at hadron colliders where theone-loop integrals appear in the loop-by-loop contributions. The four-pointintegrals are the most complicated. The ${\cal O}(\ep^2)$ expansion of thethree- and four-point integrals contains in general polylogarithms up to ${\rmLi}_4$ and functions related to multiple polylogarithms of maximal weight anddepth four.Comment: 48 pages, 4 figures in the text, slight change in the title, one  reference added, matches published versio

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

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Laurent series expansion of a class of massive scalar one-loop integrals toO(ε2)