simionx.SpecialFunctions - Special mathematical functions¶
simionx.SpecialFunctions - Special mathematical functions (e.g. elliptic integrals, error function, …).
local SF = require "simionx.SpecialFunctions" assert(SF.erf(0) == 0) assert(SF.elliptic_k(0) == math.pi/2) assert(SF.elliptic_e(0) == math.pi/2)
This module provides various special mathematical functions. They include elliptic integrals and the error function.
The complete elliptic integrals of the first and second kind are implemented in terms of the more general Carlson symmetric forms of elliptic integrals. The implementation of these functions are quite efficient and accurate (using optimized algorithms). By default, they define a maximum relative error of approximately 1e-7.
NoteThis page is abridged from the full SIMION "Supplemental Documentation" (Help file). The following additional sections can be found in the full version of this page accessible via the "Help > Supplemental Documentation" menu in SIMION 8.1.1 or above: