[seqfan] Re: Composite Hurwitz Zeta formulas for A007494 & A032766

[Neil Sloane]

Yes, go ahead and submit the two "squared" versions, and if possible upload
the nice pictures
(or, at least, give links to the pictures - but it would be better for the
long term if they were on the OEIS server)

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Thu, Nov 9, 2017 at 8:58 PM, Andras via SeqFan <seqfan at list.seqfan.eu>
wrote:

> I have two composite Hurwitz Zeta function formulas for "Numbers that are
> congruent to 0 or 2 mod 3." and "Numbers that are congruent to 0 or 1 mod
> 3." that I thought might be of some interest.
>
> My question is if these 2 sequences merit their own entries (which would
> be A007494 & A032766 squared & omitting the Sqrt function in the formula) &
> if so what they should be named, or alternatively if they should instead be
> included in the formula sections for A007494 & A032766. Here are some
> domain colored visualizations of the functions: https://i.imgur.
> com/GGPG2E0.jpg , also, if anyone knows what these types of composite
> zeta functions are named, that'd be greatly appreciated!
> Mathematica Code:
> ζ = HurwitzZeta
>
> A007494 =  Function[{Z},   Sqrt[4 - 9/2 ζ[-1, 2/3 + Z] - 3 ζ[-1, 5/6] +
>   3 ζ[-1, 4/3] + 9/2 ζ[-1, 5/3] +     3 (-1)^Z ζ[-1, 5/6 + Z/2] -     3
> (-1)^Z ζ[-1, 1/6 (2 + 3 Z)]]]
> A032766 =  Function[{Z},   Sqrt[9 - 9/2 ζ[-1, 4/3 + Z] - 3 ζ[-1, 7/6] +
>   3 ζ[-1, 5/3] + 9/2 ζ[-1, 7/3] +     3 (-1)^Z ζ[-1, 7/6 + Z/2] -     3
> (-1)^Z ζ[-1, 1/6 (4 + 3 Z)]]]
> Table[N[A007494[n]], {n, 0, 25}]
> Table[N[A032766[n]], {n, 0, 25}]
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>