ELFNCS is a special function file for the HP-41 which requires
the Advantage application ROM. It was written by Sherman Lowell.
Please see file SPFNS1T for additional remarks and references.

The ELFNCS file contains programs which compute all of the
principal elliptic integrals and Jacobian elliptic functions.
LBL"K" (local LBL A) expects the modulus k in the X-register and
returns the Complete Elliptic Integrals, K(k) and E(k), in the X-
and Y-registers, respectively. LBL"SN" (local LBL B) expects u
(in degrees) in Y-register and k, the modulus, in X-register; it
returns the four Jacobi elliptic functions: sn(u,k) in X-
register, cn(u,k) in Y-register, dn(u,k) in Z-register, and Zeta
function Z(u,k) in T-register. LBL"ELINT1" and LBL"ELINT2" expect
phi and alpha (both in degrees) in Y- and X-registers and return
the value of the Incomplete Elliptic Integrals of First and
Second Kind in X-register. LBL"ELINT3" expects phi, alpha, and
parameter n in Z, Y, X and returns the value of the Incomplete
Elliptic Integral of the Third Kind in X-register. They may also
be accessed by local labels C, D, and E in USER mode. LBL"ROOT"
is a subroutine called by the Advantage ROM function INTEG to
evaluate integrands in the elliptic integral routines. It is
necessary to set SIZE > 020 to use these programs. Accuracy of
the routines is high because of the arithmetic-geometric mean
algorithm used by all of the labels. The number of correct digits
in the result can be selected by choice of Display Mode; this
also affects runtime.

If you encounter any difficulties with these programs, please
contact the author (see file SPFNS1T.) X<>Y