Fresnel Integral

07292019, 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. 

07302019, 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. 

07302019, 08:15 PM
Post: #3




RE: Fresnel Integral
(07302019 10:35 AM)parisse Wrote: With the latest firmware, you will get (from CAS) a symbolic answer with erf and complex numbers. 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. 

07302019, 10:11 PM
Post: #4




RE: Fresnel Integral
Are we talking about the HP Prime?
Denny 

07302019, 10:37 PM
Post: #5




RE: Fresnel Integral  
07312019, 09:40 AM
Post: #6




RE: Fresnel Integral
There are no plans to add complex erf support inside limit, sorry!


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