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Fresnel integrals

Fernando Revilla

Well-known member
MHB Math Helper
Jan 29, 2012
661
I quote a unsolved question posted in MHF by user poorbutttryagin on February 5th, 2013.


I read 'functions of one complex variable by Conway'

186pg, 7.7. Prove that int_0^inf sin(t^2) dt = sqrt(pi/8)

What is the starting point?

Any comment or hint is welcomed !

Thanks !
 

Fernando Revilla

Well-known member
MHB Math Helper
Jan 29, 2012
661
Have a look at the pdf here:

120. Integrales de Fresnel | Fernando Revilla

P.S. 1 Although it is in Spanish, I think that one can follow the outline looking only at the formulas.

P.S. 2 There is a typo in the second line of the pdf.:

It should be $I_2=\displaystyle\int_0^{+\infty}\sin x^2\;dx$ instead of $I_2=\displaystyle\int_0^{+\infty}\cos x^2\;dx$
 
Last edited:

ZaidAlyafey

Well-known member
MHB Math Helper
Jan 17, 2013
1,667
I see that you are using contour integration to solve the integral .

Do you have another method to solve it ?
 

Fernando Revilla

Well-known member
MHB Math Helper
Jan 29, 2012
661