[seqfan] Re: help need with some Ramanujan identities

[Hugo Pfoertner]

Neil, Robert,
I've edited A222068 accordingly. Robert, could you please insert your sum
formulas there? A318590 can then be recycled.
Best regards
Hugo

On Fri, Aug 31, 2018 at 9:16 PM Neil Sloane <njasloane at gmail.com> wrote:

> In that case (thanks, Robert) they should definitely be merged
> 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 Fri, Aug 31, 2018 at 1:55 PM <israel at math.ubc.ca> wrote:
>
> > Modulo questions about rearrangement of non-absolutely convergent series,
> > the result should indeed be (Pi/4)^2.
> >
> > Sum_{k>=0} (-1)^k d(2k+1)/(2k+1) = Sum_{k>=0} Sum_{2i+1 | 2k+1}
> > (-1)^k/(2k+1) (letting 2k+1=(2i+1)(2j+1): note that k == i+j mod 2)
> >   = Sum_{i>=0} Sum_{j>=0} (-1)^(i+j)/((2i+1)(2j+1))
> >   = (Sum_{i>=0} (-1)^i/(2i+1))^2 = (Pi/4)^2
> >
> > Cheers,
> > Robert
> >
> > On Aug 31 2018, Hugo Pfoertner wrote:
> >
> > >Having seen Giovanni Resta's numerical results, summing 7.5*10^11 terms,
> > >one may really ask if https://oeis.org/A318590 =
> https://oeis.org/A222068
> > >and if therefore A318590 should be merged into A222068.
> > >
> > >On Wed, Aug 29, 2018 at 9:26 PM Hugo Pfoertner <yae9911 at gmail.com>
> wrote:
> > >
> > >> After summing 10^7 terms, I get 0.61685(016), which is a strange
> > >> coincidence with https://oeis.org/A222068 (Pi/4)^2=0.616850275...
> > >>
> > >> On Wed, Aug 29, 2018 at 8:21 PM Hugo Pfoertner <yae9911 at gmail.com>
> > wrote:
> > >>
> > >>> To continue with Ramanujan's questions: Question 770 dealing with
> > >>> alternating sums of d(n)=A000005 is said to have been solved in two
> > >>> articles in the Journal of the Indian Mathematical Society. Ramanujan
> > >>> had asked to show that the infinite sum d(1) - d(3)/3+ d(5)/5 -
> d(7)/7
> > >>> + d(9)/9 - ... is a convergent series. Does somebody have access to
> > the
> > >>> articles or knows about a closed form solution? From a stupid
> > summation
> > >>> of 2*10^6 terms I get for the sum: 0.61684.., which is not in the
> > OEIS,
> > >>> so I created the draft https://oeis.org/draft/A318590
> > >>>
> > >>> Hugo Pfoertner
> > >>>
> > >>>
> > >
> > >--
> > >Seqfan Mailing list - http://list.seqfan.eu/
> > >
> > >
> >
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