Riemann's Zeta Function - another approach (RPL)

[Gerson W. Barbosa]

(06-20-2017 05:04 PM)Dieter Wrote:  

(06-20-2017 02:04 AM)Gerson W. Barbosa Wrote:  What about [snip code sample] ?

This can be done with two steps less: ;-)

Code:

C01 LBL C
C02 FP
C03 ENTER
C04 1/x
C05 2
C06 LastX
C07 x!
C08 -
C09 *
C10 +
C11 RTN

I'm glad you missed my 17-step version :-)

(06-20-2017 02:04 AM)Gerson W. Barbosa Wrote:  ...for 1 < x <= 1.00001 ?

I would do the switch at the point where both methods, the regular and the simplified one, have the same error. The simplified version should be close to 12 digits with x < 1,00001, or 10 digits for x < 1,0001.

(06-20-2017 02:04 AM)Gerson W. Barbosa Wrote:  This saves the eleven steps required by the constant on the HP-11C, for instance.

On a ten digit calculator and 1 < x < 1,0001 the result has at most five decimals. So the EM-constant is not required to have more either.

Code:

01 LBL C
02 FP
03 1/x
04 ,
05 5
06 7
07 7
08 2
09 2
10 +
11 RTN

Same number of steps and faster. Sometimes I forget the good old K.I.S.S. rule. But that might be an alternative for 12-digit calculators.

I would like to see how an HP-41C implementation of what we have so far fares against existing solutions, but I'm not willing to do it myself. Maybe later.

Gerson.