Fresnel integrals are two

functions defined by:

/x
C(x) = | cos(t^2) dt
/0

and

/x
S(x) = | sin(t^2) dt
/0

Since C(infinity) = S(infinity) = sqrt(π/8), it is natural to define the complementary functions:

/inf
c(x) = sqrt(π/8) - C(x) = | cos(t^2) dt
/x

and

/inf
s(x) = sqrt(π/8) - S(x) = | sin(t^2) dt
/x