Fresnel Integrals

[salvomic]

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;

[Eddie W. Shore]

You rock, salvomic!

[salvomic]

(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