Leptonic QED Corrections to the process ep longrightarrow eX in Jaquet-Blondel variables

For the study of deep inelastic scattering at HERA, the use of Jaquet-Blondel variables is advantageous in several respects. We calculate the complete leptonic ${\cal O}(\alpha)$ QED corrections for the reaction $ep \to eX$ in these variables. All but one phase space integrations are performed analytically. After exponentiation of soft photon corrections, an accuracy of at least 1% is matched. Numerical results are presented and compared to estimates based on the leading logarithmic approximation. Equation (17) is corrected in accordance with equation (7.44) of DESY 94--115. The misprint did not influence the numerics.