erfi, erfw (w(z)) functions

[salvomic]

hi everybody,
Luckily Prime has inside its CAS two useful functions to magare problems connected to error treatment and statistics: the error function, erf() and the complementary error function, erfc().

If one want to "complete" that series, could think to implement also other two "sisters": the imaginary error function, erfi() and a function that I call "erfw", otherwise w(z) that handles every complex number.
See here for theory.

The code:
erfi()

Code:


#cas
erfi(x):=
return -i*erf(i*x)
#end

erfw()

Code:


// complex error function
#cas
erfw(x):=
return (e^-(x^2))*erfc(-i*x)
#end

Enjoy with the Prime!

Salvo Micciché