[seqfan] Re: help need with some Ramanujan identities

Hugo Pfoertner yae9911 at gmail.com
Fri Aug 31 10:25:52 CEST 2018


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
>>
>>



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