Riemann's Zeta Function - another approach (RPL)
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07-13-2017, 07:37 PM
Post: #54
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RE: Riemann's Zeta Function - another approach (RPL)
(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 |
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