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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?

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# Fresnel Integrals

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