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Updated 22 Oct 2020
Return to version 1.5 because of error in Jacobi theta function
Improved jtheta0 . Now is correct for q <= 0.999 (thanks to Alex Lee)
(1) Correction of functions JacobiTheta and jtheta
Neville theta functions are added. Two examples from mechanics are added: Euler elastica and Reissner rod
fix mpelE, add new test for melPi
Figures are included
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)
milan batista (2021). elfun18 (https://www.mathworks.com/matlabcentral/fileexchange/65915-elfun18), MATLAB Central File Exchange. Retrieved .
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