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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