Elliptic integrals

10302017, 05:27 PM
(This post was last modified: 11022017 05:29 PM by salvomic.)
Post: #1




Elliptic integrals
hi,
this is only a first attempting to make a program to handle Elliptic Integrals (1st, 2nd and 3rd kind). For theory see here. These functions haven't a control to singular values no other controls. I hope someone would like to help to implement them and to ameliorate the program. Thank you. These integrals are related with the Jacobi Elliptic Function: see here in the Library my version for it. ell1F(x, k) > F, Elliptic integral of first kind ell2E(x, k) > E, Elliptic integral of second kind ell3∏(x, k, n) > ∏, Elliptic integral of third kind *** Parameters (from Wikipedia): α, the modular angle k = sin α, the elliptic modulus or eccentricity m = k2 = sin2 α, the parameter Each of the above three quantities is completely determined by any of the others (given that they are nonnegative). Thus, they can be used interchangeably. The other argument can likewise be expressed as φ, the amplitude, or as x or u, where x = sin φ = sn u and sn is one of the Jacobian elliptic functions. Specifying the value of any one of these quantities determines the others. Note that u also depends on m. Some additional relationships involving u include *** k is the eccentricity, n is a number called "characteristic" (required only for 3rd kind) These are the "incomplete" integrals. To attempt the complete ones, put x=1... The code: Code: EXPORT ell1F(x,k) Enjoy! Salvo Micciché ∫aL√0mic (IT9CLU) :: HP Prime 50g 41CX 71b 42s 39s 35s 12C 15C  DM42, DM41X  WP34s Prime Soft. Lib 

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