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

[Gil]

I did not look at the open sources, but finally used instead https://math.stackexchange.com/questions...inary-part

creating the following HP50G function/program, that gives most acceptable results up to the last two digits (errors due to "loop roundings"), here now a mended, faster version with summation sign (sigma)

ERF(z)
« C->R -> x y
« x ERF
'e^-x^2/(2*pi*x)*(1-COS(2*x*y)+i*SIN(2*x*y))' ->NUM +
'2/pi*e^-x^2' ->NUM

'Sigma(k=1,30,e^(-k^2/4)/(k^2+4*x^2)*(2*x*(1-COS(2*x*y)*COSH(k*y))+k*SIN(2*x*y)*SINH(k*y)+i*(2*x*SIN(2*x*y)*COSH(k*y)+k*COS(2​*x*y)*SINH(k*y))))'

->NUM * + ->NUM
»
»


And ERF(x)
« 0 .5 ROT UTPN -2 * 1 +
»

The HP Prime must use a similar algorithm.