Fresnel Integrals
10-30-2017, 01:47 PM
Post: #1
 salvomic Senior Member Posts: 1,000 Joined: Jan 2015
Fresnel Integrals
hi,
this is only a first version and has'n control for singular values. I hope someone could help to do better, thank you.

Fresnel_S(x) and Fresnel_C(x) are the functions for S(x) and C(x)
Fresnel_Sn(x) and Fresnel_Cn(x) are the correspondent functions, normalised with a π/2 factor by some authors, like Abramowitz and Stegun (see here).

Enjoy!

Salvo Micciché

Code:
EXPORT Fresnel_S(x) // Fresnel integral S(x) BEGIN local t; RETURN int(SIN(t^2),t,0,x); END; EXPORT Fresnel_Sn(x) // Fresnel integral S(x) normalized π/2 BEGIN local t; RETURN int(SIN((π/2)*t^2),t,0,x); END; EXPORT Fresnel_C(x) // Fresnel integral C(x) BEGIN local t; RETURN int(COS(t^2),t,0,x); END; EXPORT Fresnel_Cn(x) // Fresnel integral C(x) normalized π/2 BEGIN local t; RETURN int(COS((π/2)*t^2),t,0,x); END;

∫aL√0 (@salvomic, IT9CLU) - HP Prime, 50g, 12C :: HP Prime Software Library
11-04-2017, 02:38 PM
Post: #2
 Eddie W. Shore Senior Member Posts: 590 Joined: Dec 2013
RE: Fresnel Integrals
You rock, salvomic!
11-04-2017, 03:55 PM
Post: #3
 salvomic Senior Member Posts: 1,000 Joined: Jan 2015
RE: Fresnel Integrals
(11-04-2017 02:38 PM)Eddie W. Shore Wrote:  You rock, salvomic!

only I try to help myself and others to have an always better Prime :-)
I think some simple enhancements should be integrated in the CAS: i.e. Fresnel, Bessel (1st, 2nd kind), Elliptic integrals (1,2,3), Surface integrals, Flux integrals... obviously with a better error control than our can do...

You're welcome!
Salvo

∫aL√0 (@salvomic, IT9CLU) - HP Prime, 50g, 12C :: HP Prime Software Library
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