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Starting with the lowest-order unscreened QED matrix element for electron-positron pair production by heavy charged particles, we calculate the cross section for this process differential in all independent variables and valid for all pair energies small compared to the incident particle energy. Plane-wave solutions to the Dirac equation are used to represent the electron and positron in this calculation. The gauge-invariance condition is used throughout the calculation to separate the cross section into quantities that reduce to the Weizsacker-Williams result in the appropriate limit and other terms that are not included in the Weizsacker-Williams approximation. The accuracy of the Weizsacker-Williams method, on which previous calculations of higher-order corrections were based, can thereby be estimated. Integration over the possible emission angles of one of the pair members gives an expression valid for low-energy pairs that can be compared with previous work based on the Weizsacker-Williams method. Integration over the possible angles of the other pair member then gives an expression that turns out to be identical to one derived by Racah, as we show in detail, although some of the expressions given here prior to the second angular integration have not been given previously. The high energy-transfer limit of the expression for the cross section integrated over electron and positron angles is shown to be identical to that of Kelner in the unscreened case. Additional numerical integrations over the remaining variables are performed for a range of projectile energies using Kelner's treatment of screening. These examples allow the determination of the accuracy of the Weizsacker-Williams method as previously applied as a function of projectile and pair energy. The results for the total cross section, which include the correct behavior for low energy transfers, are compared with previous calculations.

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