Fresnel Integral - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Calculators (and very old HP Computers) (/forum-3.html) +--- Forum: HP Prime (/forum-5.html) +--- Thread: Fresnel Integral (/thread-13374.html) Fresnel Integral - LCieParagon - 07-29-2019 10:42 PM 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. RE: Fresnel Integral - parisse - 07-30-2019 10:35 AM 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. RE: Fresnel Integral - LCieParagon - 07-30-2019 08:15 PM (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. RE: Fresnel Integral - Leviset - 07-30-2019 10:11 PM Are we talking about the HP Prime? RE: Fresnel Integral - LCieParagon - 07-30-2019 10:37 PM (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. RE: Fresnel Integral - parisse - 07-31-2019 09:40 AM There are no plans to add complex erf support inside limit, sorry!