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Fresnel Integral
07-29-2019, 10:42 PM
Post: #1
Fresnel Integral
Hello. I have a question.

Is there any plans to implement the Fresnel Integral into the HP Calculator?

For example, when I try to compute:
integral(cos(x^2),x,0,t) I get rather strange results.
For instance, if I choose t to be 2, I receive 0.46146...
If I choose t to be 1000, I receive a 1x2 vector: [-1.9805..., 10.78289...]
Clearly, a definite integral is not a 1x2 vector, it is in fact a number.

Moreover, if t approaches infinity, the value should be (1/2) * sqrt(pi/2). I receive a 1x2 vector again.

If I could have any help on the matter, I'd appreciate it. Thanks.
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07-30-2019, 10:35 AM
Post: #2
RE: Fresnel Integral
With the latest firmware, you will get (from CAS) a symbolic answer with erf and complex numbers.
int(cos(x^2),x,0,t)
int(cos(x^2),x,0,1000);
evalf(int(cos(x^2),x,0,1000))
If you try to compute the integral numerically:
int(cos(x^2),x,0,1000.0)
the quadrature fails because the integrand is varying much too fast (especially near 1000), this is why you get a warning on the terminal, and the answer returned is a vector of 2 values corresponding to the last computed approximations.
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07-30-2019, 08:15 PM
Post: #3
RE: Fresnel Integral
(07-30-2019 10:35 AM)parisse Wrote:  With the latest firmware, you will get (from CAS) a symbolic answer with erf and complex numbers.
int(cos(x^2),x,0,t)
int(cos(x^2),x,0,1000);
evalf(int(cos(x^2),x,0,1000))
If you try to compute the integral numerically:
int(cos(x^2),x,0,1000.0)
the quadrature fails because the integrand is varying much too fast (especially near 1000), this is why you get a warning on the terminal, and the answer returned is a vector of 2 values corresponding to the last computed approximations.

Thanks, I updated my firmware.

Are there any plans to have it work with infinity? I get an error message stating that erf is not yet supported with complex values and limits.

Just curious, thanks.
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07-30-2019, 10:11 PM
Post: #4
RE: Fresnel Integral
Are we talking about the HP Prime?

Denny
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07-30-2019, 10:37 PM
Post: #5
RE: Fresnel Integral
(07-30-2019 10:11 PM)Leviset Wrote:  Are we talking about the HP Prime?

Yes. The HP Prime. I have the symbolic result of the Fresnel Integral now, but I still don't have the ability to find the limit as x --> Infinity

It states that the HP Prime has not yet implemented it yet.
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07-31-2019, 09:40 AM
Post: #6
RE: Fresnel Integral
There are no plans to add complex erf support inside limit, sorry!
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