Riemann's Zeta Function - another approach (RPL)

[Dieter]

(07-13-2017 12:27 PM)John Keith Wrote:  Very impressive! I compared your results with those of the Prime. All the values agree except for 0.8, for which the Prime returns -4.43753841590. I assume the Prime is in error here?

The Prime is correct. The difference between the two values is the result of different rounding:

(07-13-2017 12:27 PM)John Keith Wrote:  Edit: just checked Wolfram Alpha, your result is accurate to 11 digits (actual value -4.43753841589555...).

Yes, that's the exact result. The 13th digit is a 5, so it gets rounded up. On the other hand the approxmation yields -4.43753841589483... which rounds down. The actual difference is merely 7 units in the 14th significant digit, but that close to the rounding threshold this can make a difference in the last place.

This can also happen with the built-in functions. Take sin 34,444° = 0,5656004784499... which rounds up to 0,5656004785 on an HP 67, 41C or 15C. Here one unit in the 13th digit can make a difference on a 10-digit calculator. ;-)

Dieter