Erfi function

It has series about z=given by. Introduction to the probability integrals and inverses. The probability integral (error function ) has a long history beginning with the articles of A. En matemáticas, la función error (también conocida como función error de Gauss ) es una función especial (no elemental) que se utiliza en el campo de la probabilida la estadística y las ecuaciones diferenciales parciales. In MuPAD Notebook only, computes the imaginary error function.

The initial conditions of ERFI. Octave-Forge is a collection of packages providing extra functionality for GNU Octave. The complementary error function.

The Erfi function and the Dawson integral Definition of the Erfi function. In some applications we find 2. Imaginary error function , -i erf(i z). Looking for abbreviations of ERFI? While Excel has a built in efr error function it has no imaginary error function erfi. Clearly we cannot perform a summation to infinity.

Also the scipy implementation gives me a real value too. This is entirely real valued! Yes I see the reference code, but it is pretty much impossible to follow.

How can I implement the erfi function using the incomplete Gamma representation and still get a real . Unfortunately, in SciPy 0. Repeated Integrals of the Error Function. These functions use the mpmathlibrary for numerical evaluation and Maxima, Pynac for symbolics. Real or complex number(s), the value(s) of the function.

Description the Faddeeva function the scaled complementary error function the error function of complex arguments the imaginary error function the complementary error function the Dawson function. Faddeeva_w(z, relerr = 0) erfcx(z, relerr = 0) erf(z, relerr = 0) erfi(z, relerr = 0) erfc(z, relerr = 0). THE ERROR FUNCTION erf(x) AND ITS COMPLEMENT erfc(x) Inverse error function. THE AND RELATED FUNCTIONS Properties in the complex plane and the Voigt function.

I need to use the imaginary error function in fitting routines. The error function , defined as: Erf(x)=2π−−√∫x0e−t2dt. Some publications use the erfc(x) function , which is defined as 1-Erf(x). A separate Erfc function is not built into Analytica.

Another variation that appears is some publications is the erfi(x) function. Erfi is a real-valued function when . Given the Faddeeva function w(z) and the other complex error functions, one can also easily . Returns: A scalar or series, the value of erfi(z) = -i erf(iz). Example: erfi(-.0);.