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You are not logged in. #1 20121102 06:46:06
Fresnel Integrals via Differentiation Under Integral SignI've been trying to do and using DUIS, but I can't think of any kind of useful parametrisation that would work. Every time I do, I usually end up with something that *looks* like you can use integration by parts, but that doesn't work. I'm aware the indefinite integral form of these integrals can't be expressed in terms of elementary functions, so I'm hoping I might have more luck with the improper ones. Can anyone show me a useful parametrisation that would work here? #2 20121102 07:55:11
Re: Fresnel Integrals via Differentiation Under Integral SignHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #3 20121102 07:58:22
Re: Fresnel Integrals via Differentiation Under Integral SignThe last page here says you can do it. #4 20121102 08:00:59
Re: Fresnel Integrals via Differentiation Under Integral SignHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #5 20121102 08:02:18
Re: Fresnel Integrals via Differentiation Under Integral SignI know you can do it without DUIS (e.g. gamma function method), but was curious if it was made really simple via DUIS (like integrating sinx/x). #6 20121102 08:05:54
Re: Fresnel Integrals via Differentiation Under Integral SignHi;
If you meant the examples at the end of that pdf then it meant and not the integral you want. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #7 20121102 08:07:06
Re: Fresnel Integrals via Differentiation Under Integral SignBut that is not a Fresnel integral. They said that the middle row contains two Fresnel integrals... so either they meant that it does not contain two Fresnel integrals, or they didn't parenthesise the powers properly... #8 20121102 08:12:25
Re: Fresnel Integrals via Differentiation Under Integral SignThose are not Fresnel integrals so he made one of two mistakes. He did not put the square in the proper spot or he does not know what a Fresnel Integral is. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #9 20121102 08:16:30
Re: Fresnel Integrals via Differentiation Under Integral SignHmm. So, there might not be a way. I will still try to look for one however. It seems I never get to use this little tool. #10 20121102 22:00:29
Re: Fresnel Integrals via Differentiation Under Integral SignHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11 20121102 22:02:09
Re: Fresnel Integrals via Differentiation Under Integral SignWhat sorts did you try? I tried something of the form ln(bsinx^{2}) or similar, in the hope that I could cancel the trig term, but it did not work. Maybe trying to use a trig identity would fare better? #12 20121102 22:10:02
Re: Fresnel Integrals via Differentiation Under Integral SignI tried that one and also sin(x^b). In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. 