Based on the angular spectrum decomposition method in plane waves, a generalized nonparaxial analytical solution for the electric field of a transverse electric Airy light-sheet including its spatial derivatives is formulated and presented. The beam-shape coefficients are expressed by an improper integral, which includes the generation of evanescent waves. The radiated component of the field is computed, and the cross-sectional plots display unique features of the nonparaxial Airy light-sheet and its higher-order derivatives. The results find important applications in predicting/computing the optical scattering, radiation force, and torque on an object using the multipole expansion method in cylindrical coordinates and particle dynamics.