elfun18

elfun18 is a set of functions that enable computation of various elliptic integrals and functions.

elfun18 is a collection of Matlab functions that enable the computation of wide set of Elliptic integrals, Jacobi's elliptic functions and Jacobi's theta functions for real arguments. The set has two levels: higher level functions with matrix arguments and low level functions with scalar arguments. Each function is available either with the modulus k or parameter m as argument. In later case the function name begin with m. Incomplete elliptic integrals are given in Jacobi form, Legendre form and Jacobi's second form (Epsilon function and Lambda functions).
List of functions:
Elliptic integrals:
- Bulirsch's elliptic integrals: cel, cel1, cel2, cel3, el1, el2, el3
- Carlson's elliptic integrals: rc, rd, rf, rg, rj
- Complete elliptic integrals: B, C, D, K, E, Pi
- Complementary complete elliptic integrals: K', E', Pi'
- Jacobi form of elliptic integrals: B, D, E, F, Pi
- Legendre form of elliptic integrals: B, D, E, F, Pi
- Jacobi second form of elliptic integrals: Epsilon, Zeta ( periodic part of Eps) Lambda ( elip. int. of 3rd kind), Omega
function ( periodic part of Lambda)
Jacobian elliptic functions
- am, cd, cn, cs, dc, dn, ds, nc, nd, ns, sc, sd, sn

Inverse Jacobian elliptic functions
- invam, invcd, invcn, invcs, invdc, invdn, invds, invnc, invnd, invns, invsc, invsd, invsn

Jacobi Theta Functions
- theta1, thet12, theta3, theta4, nome, modulus
Neville theta functions
-nthetac, nthetad, nthetan, nthetas
Misc. functions
- agm ( arithmetic geometric mean), cl (lemniscate cos), sl, (lemniscate sin), invcl (inverse lemniscate cos), invsl (inverse lemniscate sin), Lambda0 (Heuman's function) gd (Gudermannian function), invgd (inverse Gudermannian function)