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:
- 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
- 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)
For finding current line handle
Nevermind, I found your arxiv article that explained that I'm looking for mpEllipticE. Thanks!
What is the relationship between mEllipticE(u,m) and Matlab's symbolic toolbox's ellipticE? Thanks!
jacobiCN(x,m) use m as the parameter while JacobiCN(x,k) use elliptic modulus k as the parameter. So you should use mJacobiCN(x,m). Then you will obtain the same results as by jacobiCN . For example mJacobiCN(2,0.5)=-0.103183615527762 and jacobiCN(2,0.5) = -0.103183615527762
Could you tell me why the result from your function is different from the result from the matlab?
for example:JacobiCN and jacobiCN .
Thank you very much!
Add note about Neville theta function
Neville theta functions are added. Two examples from mechanics are added: Euler elastica and Reissner rod
Correct mijns.m and InverseJacobiAM_doc.mlx
Major revision. Add live script examples.
Fix melK and mpelF.
fix mpelE, add new test for melPi
Fix bugs in mjlambda.m
Figures are included
Create scripts with code, output, and formatted text in a single executable document.