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Time to make it a "real" answer :

As of Sage 8.3 (released Aug, 3, 2018), Sage implements :

• fresnels_sin (i. e. $\displaystyle\int_0^x \sin\frac{\pi t^2}{2} dt$), and

• fresnels_cos (i. e. $\displaystyle\int_0^x \cos\frac{\pi t^2}{2} dt$).

Note that Sage follows DLMF's (a. k Abramowitz & Stegun) definitions rather that the simpler ones quoted by (the start of the) Wikipedia article. Note also that this does not implement Frenel's $\cal{F}(z)=\displaystyle\int_z^\infty \textrm{e}^{\frac{1}{2}\pi i t^2} \textrm{d}t $ (left as an exercise to the reader ?).

Time to make it a "real" answer :

As of Sage 8.3 (released Aug, 3, 2018), Sage implements :

• fresnels_sin (i. e. $\displaystyle\int_0^x \sin\frac{\pi t^2}{2} dt$), and

• fresnels_cos (i. e. $\displaystyle\int_0^x \cos\frac{\pi t^2}{2} dt$).

Note that Sage follows DLMF's (a. k Abramowitz & Stegun) definitions rather that the simpler ones quoted by (the start of the) Wikipedia article. Note also that this does not implement Frenel's Fresnel's $\cal{F}(z)=\displaystyle\int_z^\infty \textrm{e}^{\frac{1}{2}\pi i t^2} \textrm{d}t $ (left as an exercise to the reader ?).

Time to make it a "real" answer :

As of Sage 8.3 (released Aug, 3, 2018), Sage implements :

• fresnels_sin (i. e. $\displaystyle\int_0^x \sin\frac{\pi t^2}{2} dt$), and

• fresnels_cos (i. e. $\displaystyle\int_0^x \cos\frac{\pi t^2}{2} dt$).

Note that Sage follows DLMF's (a. k k. a. Abramowitz & Stegun) definitions rather that the simpler ones quoted by (the start of the) Wikipedia article. Note also that this does not implement Fresnel's $\cal{F}(z)=\displaystyle\int_z^\infty \textrm{e}^{\frac{1}{2}\pi i t^2} \textrm{d}t $ (left as an exercise to the reader ?).

Time to make it a "real" answer :

As of Sage 8.3 (released Aug, 3, 2018), Sage implements :

• fresnels_sinfresnel_sin (i. e. $\displaystyle\int_0^x \sin\frac{\pi t^2}{2} dt$), and

• fresnels_cosfresnel_cos (i. e. $\displaystyle\int_0^x \cos\frac{\pi t^2}{2} dt$).

Note that Sage follows DLMF's (a. k. a. Abramowitz & Stegun) definitions rather that the simpler ones quoted by (the start of the) Wikipedia article. Note also that this does not implement Fresnel's $\cal{F}(z)=\displaystyle\int_z^\infty \textrm{e}^{\frac{1}{2}\pi i t^2} \textrm{d}t $ (left as an exercise to the reader ?).