Linked Questions

0
votes
1answer
183 views

Trying to compute erfcx(x)? [duplicate]

The function erfcx(x) = exp(x^2)erfc(x) is sometimes provided in numerical packages to avoid numerical underflow for large values of ...
38
votes
2answers
1k views

Is it possible to make Mathematica reformulate an expression in a more numerically stable way?

I'm writing a numerical optimization, and I'm having a problem with an expression of the form $$ e^{-t} (1+\mathrm{erf}(t)) $$ The overall shape of the function looks correct, but when $t$ is small, $...
14
votes
4answers
1k views

Implementing a compilable Faddeeva function of complex argument

For those, who are looking at Halirutan's answer and thinking "gee, I wish I was that good at LibraryLink, then I could really speed up my code!" I leave here the ...
14
votes
4answers
533 views

Terrible accuracy of DawsonF

DawsonF[30.] returns 0. The correct value is 0.016676... At least it prints a warning message, ...
3
votes
3answers
404 views

How can I compute Erf of large numbers to more precision?

I would like to compute Erf[80/3] to enough precision to know the order of magnitude of 1 - Erf[80/3] How can I do that? I ...
8
votes
2answers
706 views

Analytical approximation of indefinite integral on a given interval to a given precision

I'm looking for an analytical approximation of $\int_a^b e^{-x^2}\mathrm{erf}(x+c) dx$ that would be accurate to precision $\varepsilon$ for $a,b,c$ within a certain range. How do I ask Mathematica ...
4
votes
2answers
1k views

How to find the maximum of this function on the positive real line?

I need to maximize this function on the positive real line: $$ \frac{1}{\Gamma(x)^{14}}\cdot\frac{1}{{\frac{323.6}{14x}}^{14x}}\cdot(1.22578*10^{19})^{x-1}e^{-14x} $$ the correct answer should be ...
4
votes
2answers
927 views

Assigning an analytical approximation to the error function erf(x)

Working with some iterative integral equations, I have Gaussian density functions involved therein. Integrating the Gaussian function I obtain the error function. When I take the second integration, ...
1
vote
1answer
1k views

Error Function Integral (Erf)

Any idea how to solve analytically this integral Integrate[(a Erf[a Sqrt[b/(a^2 + b)] c])/(a^2 + b)^(3/2), a] I tried substitution u=a^2 + b, but it didn't work. ...
1
vote
1answer
276 views

Calculate an integration limit to obtain a certain area under a curve

I have a function that looks like a sigmoid curve. I would like to calculate the right integration limit so that the area under the sigmoid curve has a given value. my curve: ...