Fresnel integral definitions and function composition

[Barkan]

Hello everyone,

I am currently dealing with some coupled differential equations. Seems like the result include Fresnel integrals which are easy to be approximated.

However, I am confused in many ways and I hope some experienced people can answer following:

1) Normally, we can obtain real numbers' fresnel integral values meaning:

FresnelS(a) = int(sin(t^2),t , 0, a) where a is a real value.

What happens if I want to compute some function's fresnel integral?

FresnelS(t) for example

2) What is the correct definition of Fresnel integrals. Some say FresnelS= int(sin(t^2)) and others say FresnelS = int(pi/2 * (sin(t^2)))

3) MATLAB gives a solution including FresnelC and FresnelS. But Matlab does not have any function to deal with fresnels. Anyway, which definition (shown above) does Matlab use?

 

[lurflurf]

There is no standard definition. You just need to know which one is being used each time. Try to figure it out by looking in the documentation or computing a few values.

 

[Barkan]

Actually, I still don't know which definition does Matlab use. But -as you said- it should be asy to understand by trying some numeric values. I guess.

As I solved my own problem, I should answer my own questions.

i)What happens if I want to compute some function's fresnel integral?
Answer: Nothing special. For example you have a time vector like t=0.0:0.001:10
and you can calculate this vector's FresnelS and FresnelC straightforward.

If you go to MATLAB central, there are many good works to compute Fresnel Integrals in matlab.