Elliptic integrals

11022017, 05:42 PM
(This post was last modified: 11022017 05:54 PM by salvomic.)
Post: #2




RE: Elliptic integrals
These integrals are related to the Jacobi Elliptic Function (see in Wikipedia).
See here in the Library my version for the Prime. About the two version of 1st kind integral I used in the two programs, they are related, being the same integral: x = sin(φ), then φ=ASIN(x), m=k^2... The relation involve also sn(), cn(), dn() [sometimes called amplitude sine, amplitude cosine, delta amplitude However I get values a bit different (see attachment): what kind of rounding is responsible of the difference, in this case? A part of the examples in the attached image, another example: in the first case for the function ell1F() I test x=1 k=0.4 then ell1F(1,0.4) that returns 1.63999977306; in the second case (Jacobi) for the function Jacobi_fn() I test φ=ASIN(x), m=0.4^2 that returns 1.63999986587... First case: the integral is int(1/(SQRT((1t^2)*(1(k^2)*t^2))),t,0,x); Second case: the integral is int(1/(SQRT(1m*SIN(θ)*SIN(θ))),θ,0,φ). The *should* be the same value. laTeX form (Wikipedia): 1st form 2nd form What about it? Salvo ∫aL√0mic (IT9CLU) :: HP Prime 50g 41CX 71b 42s 39s 35s 12C 15C  DM42, DM41X  WP34s Prime Soft. Lib 

« Next Oldest  Next Newest »

Messages In This Thread 
Elliptic integrals  salvomic  11012017, 10:00 AM
RE: Elliptic integrals  salvomic  11022017 05:42 PM
RE: Elliptic integrals  AlexFekken  11032017, 01:54 PM
RE: Elliptic integrals  salvomic  11032017, 03:41 PM
RE: Elliptic integrals  Eddie W. Shore  11072017, 12:51 PM
RE: Elliptic integrals  salvomic  11072017, 01:30 PM

User(s) browsing this thread: 1 Guest(s)