zeta for imaginary numbers > 80

[christofelfferich]

Hi Paul, the zeta function returns NaN for complex numbers with Im>80. It seems that the factorial product overflows. Would this algorithm be suitable for Imaginary numbers > 80? This complex implementation of the zeta function has been my favorite and I would prefer to resolve this issue for plotting output values for imaginary inputs up to 1000. Thanks!

[paulmasson]

@christofelfferich I'm sure that is factorial( 2*i ) overflowing. The Borwein approximation has its limits that far up the imaginary axis. I'll try some adjustments later this week to see how far I can push it.

[christofelfferich]

Hi Paul, That would be great. I will have a look as well to see if I can help. Below a visual for this case of overflowing.

[paulmasson]

@christofelfferich I tried truncating the Borwein series at the first overflowing term, but that just led to incorrect results. There's not much I can do with vanilla JavaScript until it supports BigNumber. While there are existing big number libraries, I don't want add that overhead when my library is intended to run efficiently in browsers.

I'll leave this issue open for awhile to remind myself of the limitation. You're welcome to adapt my code to a library that supports big numbers for your own use.

[christofelfferich]

@paulmasson Thank you for your effort. I agree BigNumber would be a good resort for this minor limitation. I will remain happily exploring your library and might look into some adaptations in the future. Best regards.