Fowler-Nordheim parameters for sharply-curved emitters

A brief program has thus been written that can evaluate the JWKB integral for any barrier potential energy V(x) that can be expressed in the form of a ratio P(x)/Q(x) of two power series not exceeding ten terms each. By working in double-precision arithmetic on a server, the result can be obtained to a precision of about 15 significant figures. By contrast, elliptic functions are normally tabulated to a precision of 2 parts in 10⁸, so (except for the elementary triangular barrier case) there seems little useful purpose in using analytical solutions to the JWKB integral, even for the standard Schottky-Nordheim barrier.