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We derive an analytic form for the Heisenberg-Euler Lagrangian in the limitwhere the component of the electric field parallel to the magnetic field issmall. We expand these analytic functions to all orders in the field strength($F_{\mu\nu}F^{\mu\nu}$) in the limits of weak and strong fields, and use thesefunctions to estimate the pair-production rate in arbitrarily strong electricfields and the photon-splitting rate in arbitrarily strong magnetic fields.Comment: ReVTeX, 9 pages, 4 figures, to be published in Phys. Rev.

Analytic form for the effective Lagrangian of QED and its application to pair production and photon splitting