RE: HP48-HP50G : Error functions ERF(z), FRESNEL integrals, PROBIT, etc.

[Gil]

About Albert's version:

It's the one I use from the very beginning.
The published version is the derived one
(c —> complementary, ie "1-...").

For clarity, here are my non modified versions for argument a real number:

ERF
« 0 .5 ROT UTPN -2 * 1 +
»

iERF (reversed operations)
« 1 - -2 / —> p
«
« p 0 .5 X UTPN -
» 'X' 2 ROOT "x of Erf" —>TAG
»
»

ERFc
« 0 .5 ROT UTPN 2 *
»

iERFc (reversed operations)
« 2 / —> p
«
« p 0 .5 X UTPN -
» 'X' 2 ROOT "x of Erfc" —>TAG
»
»

Question 1:
Is there an elegant way to solve for the introduced variable X without creating that new variable (that I can of course delete at the end of the programs iERF and iERFc by 'X' PURGE)?

Question 2:
How could I calculate erf(i*x) for x=0.5 in
'2/sqrt(pi)*S(0.,.5*i,e^-t^2.,t)' ?
A way should be to implement the explanations given in
https://math.stackexchange.com/questions...inary-part

Observation:
The Nspire CX II-T CAS from TI seems to give 14 correct digits for the corresponding integral, versus "only" 13 digits with the built-in erf/erfc functions of the Prime calculator from HP.

For Erf(z a complex) & erfc(z), see below.