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

[Gil]

New version 16.08

3 not at all important changes:

a) clearer explanations at the beginning of
- FRESNEL.z main program
- & subroutine function FRESNEL...;

b) change of the name of the above subroutine into:
- 'fresnelFASTxLARGE' (at the end, preference was given to small initial letters, indicating clearly that fresnel is a subroutine);

c) of course, FRESNEL.z refers now consequently to
new name fresnelFASTxLARGE.

Though meaningless or useless, here are some results found by the HP50G programs that might be compared with Wolfram Alpha:

{"ERF
c


(
33
)
" 1.93206244519E-475
"ERF

(
33
)
" 1. "

" "
Inv
ERF
c


(
1.93206244519E-475
)
" 33. "

" "Probit

(
1
)
" '+infinity' "

" "
i¹
ERF
c


(
5
)
" :Wiki (Wolframopp): 1.4813429336E-13 "

" "
i¹
ERF
c


(
+infinity 
)
" "Undef by Wolfram
as '0/0' (or —>0:
try 
i¹
ERF
c
(x) with
x=10 x=20 x=33)" "

" "
i¹
ERF
c


(
-infinity 
)
" :Wiki (Wolfram—>opp): '+infinity ' "

" "
i²
ERF
c


(
25
)
" :Wiki (Wolfram—>opp): 3.3068803E-277 "

" "
normaliz
.FRESNEL
S


(
10
)
" .468169978589 "

normaliz
.FRESNEL
C


(
10
)
" .499898694222 "

" "fresnelFASTxLARGE" "
normaliz
.FRESNEL
S


(
5000*e^(pi*i)
=-5000
)
" -.499936338031 "


normaliz
.FRESNEL
C


(
5000*e^(pi*i)
=-5000
)
" -.500000002602 "

" "fresnelFASTxLARGE" "
normaliz
.FRESNEL
S


(
500000000000
)
" .5 "


normaliz
.FRESNEL
C


(
500000000000
)
" .500000000001 "

" "
normaliz
.FRESNEL
S


(
-infinity 
)
" '-1/2' "


normaliz
.FRESNEL
C


(
-infinity 
)
" '-1/2' "

" "
not
_norm.FRESNEL
S


(
+infinity 
)
" 'sqrt(2*pi)/4' "


not
_norm.FRESNEL
C


(
+infinity 
)
" 'sqrt(2*pi)/4' "

" "ERF
i


(
(4.,2.)
)
" (-20442.123626,3999.26730293) "

" "ERF
i


(
4+2*i
=(4.,2.)
)
" (-20442.123626,3999.26730293) "

" "ERF
cx


(
(5.,0.)
=5
)
" .110704637733 "

" "
w
_
F
aaddeva-Kramp

(
5
)
" (1.3887943865E-11,.11524596183) "

" "
F
_Dawson

(
5
)
" .102134074424 "

" "P
(
X>
h
 & 0<Y<
a
X
)
:
Owen_T

(
h=5,
a=3
)
" 1.4332578594E-7

Enjoy the use of the differents function with your HP50G phone application!