Hickerson series of almost integers: Difference between revisions
Content added Content deleted
m (→version 2: added whitespace, simplified the wording in the REXX section header.) |
m (→version 3: added whitespace.) |
||
| Line 2,033: | Line 2,033: | ||
This REXX version takes advantage that the Hickerson series are computed in order, so that the factorials need not be (re-)computed from scratch. |
This REXX version takes advantage that the Hickerson series are computed in order, so that the factorials need not be (re-)computed from scratch. |
||
<lang rexx>/*REXX program to calculate and show the Hickerson series (are near integer). */ |
<lang rexx>/*REXX program to calculate and show the Hickerson series (are near integer). */ |
||
numeric digits length(ln2()) |
numeric digits length(ln2())-length(.) /*be able to calculate big factorials. */ |
||
parse arg N . /*get optional number of values to use.*/ |
parse arg N . /*get optional number of values to use.*/ |
||
if N=='' then N= |
if N=='' then N= 1 /*Not specified? Then use the default.*/ |
||
!= |
!= 1 /* [↓] compute possible Hickerson #s. */ |
||
do j=1 for N; #=Hickerson(j) |
do j=1 for N; #= Hickerson(j) /*traipse thru a range of Hickerson #s.*/ |
||
?=right(#*10%1, 1) |
?= right(# * 10 % 1, 1) /*get 1st decimal digit past dec. point*/ |
||
if ?==0 | ?==9 then _= 'almost integer' /*the number is, */ |
if ?==0 | ?==9 then _= 'almost integer' /*the number is, */ |
||
else _= ' ' /* or it ain't. */ |
else _= ' ' /* or it ain't. */ |
||
say right(j,3) _ format(#,,5) |
say right(j,3) _ format(#, , 5) /*show number with 5 dec digs fraction.*/ |
||
end /*j*/ |
end /*j*/ |
||
exit /*stick a fork in it, we're all done. */ |
exit /*stick a fork in it, we're all done. */ |
||
/*─────────────────────────────────────────────────────────────────────────────────────────────────────────*/ |
/*─────────────────────────────────────────────────────────────────────────────────────────────────────────*/ |
||
Hickerson: parse arg z; !=!*z; return ! / (2*ln2() ** (z+1)) |
Hickerson: parse arg z; != ! * z; return ! / (2*ln2() ** (z+1) ) |
||
ln2: return .69314718055994530941723212145817656807550013436025525412068000949339362196969471560586332699641, |
ln2: return .69314718055994530941723212145817656807550013436025525412068000949339362196969471560586332699641, |
||
|| 8687542001481020570685733685520235758130557032670751635075961930727570828371435190307038623891673471123, |
|| 8687542001481020570685733685520235758130557032670751635075961930727570828371435190307038623891673471123, |
||