  In the study of conformal field theories, conformal blocks in the lightcone
limit are fundamental to the analytic conformal bootstrap method. Here we
consider the lightcone limit of 4-point functions of generic scalar primaries.
Based on the nonperturbative pole structure in spin of Lorentzian inversion, we
propose the natural basis functions for cross-channel conformal blocks. In this
new basis, we find a closed-form expression for crossed conformal blocks in
terms of the Kamp\'e de F\'eriet function, which applies to intermediate
operators of arbitrary spin in general dimensions. We derive the general
Lorentzian inversion for the case of identical external scaling dimensions. Our
results for the lightcone limit also shed light on the complete analytic
structure of conformal blocks in the lightcone expansion.
