[seqfan] Re: Some conjectured relations in the database (involving Ramanujan's functions)

[Thomas Baruchel]

On Sat, 16 Dec 2017, Neil Sloane wrote:
> Thomas, That's very interesting!

Thank you for this comment, Neil!

If some people are interested, I put ontline my code (written in standard C;
the very single required library being zlib): see https://github.com/baruchel/oeis

Just compile it after having set the main constants at the beginning of the file
and put the executable in the same directory than names.gz and stripped.gz. You can
get many similar relations (see below) related to the same "keyword" or not.

> The thing to do would be to add a line like this to the FORMULA section of
> each of the sequence involved, saying something like

OK, I will try to do it during the week to come.

> But you realize that by focusing on Ramanujan, you have entered into a
> field, elliptic functions and theta series, where there are
> an incredibly huge number of known identities, going back hundreds of years

As I said, I am going to explore other areas.

> record somewhere (perhaps create a page on the OEIS Wiki where you can list
> them all).  But you might find more gold nuggets

Maybe I could create a page related to my software and put various sections in
it according to the used Regex (here was "ramanujan"). But I don't know exactly
how to create such a page; where should I start from? Do I have the required rights
for creating such a page? etc.

I rewrote my code in C for making it more efficient; fortunately I previously
converted the PSLQ algorithm into a C macro at:

   https://github.com/baruchel/numerical-routines/tree/master/c

which made me spare a lot of time. With the code at https://github.com/baruchel/oeis
(as said at the beginning of this message), compiled with

     #define NBR 5
     #define ATLEAST 4

and run with   ./oeis-lindep54 "ramanujan" I could get new identities involving four
sequences:

A138518 A138522 A261988 A294387    -->    -1 -4 15 -10    (342)
A138518 Expansion of (phi(-q) / phi(-q^5))^2 in powers of q where phi() is a Ramanujan theta function.
A138522 Expansion of f(q, q^3)^2 / (f(q, q^4) * f(q^2, q^3)) in powers of q where f(, ) is the Ramanujan general theta function.
A261988 Expansion of phi(q^9) / phi(q) in powers of q where phi() is a Ramanujan theta function.
A294387 Expansion of chi(q^3) / chi^3(q) in powers of q where chi() is a Ramanujan theta function.

A256014 A256282 A258210 A258279    -->    -1 1 -1 1    (4)
A256014 Expansion of phi(-q^3)^4 / (phi(-q) * phi(-q^9)) in powers of q where phi() is a Ramanujan theta function.
A256282 Expansion of f(-q^3) * psi(q^3)^3 / (psi(q) * psi(q^9)) in powers of q where psi(), f() are Ramanujan theta functions.
A258210 Expansion of f(-q) * f(-q^2) * chi(-q^3) in powers of q where chi(), f() are Ramanujan theta functions.
A258279 Expansion of psi(q)^2 * chi(-q^3)^2 in powers of q where psi(), chi() are Ramanujan theta functions.

A113660 A113973 A253623 A253625    -->    -1 3 2 -4    (30)
A113660 Expansion of phi(x)^3 / phi(x^3) where phi() is a Ramanujan theta function.
A113973 Expansion of phi(x^3)^3/phi(x) where phi() is a Ramanujan theta function.
A253623 Expansion of phi(q) * f(q, q^2)^2 / f(q^2, q^4) in powers of q where phi(), f() are Ramanujan theta functions.
A253625 Expansion of psi(q^2) * f(-q, q^2)^2 / f(-q, -q^5) in powers of q where psi(), f() are Ramanujan theta functions.

A115978 A122859 A253623 A253625    -->    -5 -1 -2 8    (94)
A115978 Expansion of phi(-q) * phi(-q^3) in powers of q where phi() is a Ramanujan theta function.
A122859 Expansion of phi(-q)^3 / phi(-q^3) in powers of q where phi() is a Ramanujan theta function.
A253623 Expansion of phi(q) * f(q, q^2)^2 / f(q^2, q^4) in powers of q where phi(), f() are Ramanujan theta functions.
A253625 Expansion of psi(q^2) * f(-q, q^2)^2 / f(-q, -q^5) in powers of q where psi(), f() are Ramanujan theta functions.

A128144 A132972 A213267 A261156    -->    2 3 -3 -2    (26)
A128144 Expansion of chi(-q)* chi(-q^2)* chi(-q^9)/( chi(-q^3)* chi(q^9)) in powers of q where chi() is a Ramanujan theta function.
A132972 Expansion of chi(q)^3 / chi(q^3) in powers of q where chi() is a Ramanujan theta function.
A213267 Expansion of phi(q^9) / (psi(-q) * chi(q^3)) in powers of q where phi(), psi(), chi() are Ramanujan theta functions.
A261156 Expansion of chi(q) * chi(-q^9) / (chi(-q) * chi(q^9)) in powers of q where chi() is a Ramanujan theta function.

A128128 A128770 A138518 A138522    -->    10 -15 1 4    (342)
A128128 Expansion of chi(-q^3) / chi^3(-q) in powers of q where chi() is a Ramanujan theta function.
A128770 Expansion of phi(-q^9) / phi(-q) in powers of q where phi() is a Ramanujan theta function.
A138518 Expansion of (phi(-q) / phi(-q^5))^2 in powers of q where phi() is a Ramanujan theta function.
A138522 Expansion of f(q, q^3)^2 / (f(q, q^4) * f(q^2, q^3)) in powers of q where f(, ) is the Ramanujan general theta function.

A128144 A128145 A145727 A145782    -->    1 1 -1 -1    (4)
A128144 Expansion of chi(-q)* chi(-q^2)* chi(-q^9)/( chi(-q^3)* chi(q^9)) in powers of q where chi() is a Ramanujan theta function.
A128145 Expansion of psi(q^3)* phi(-q^3)* chi^2(-q^3)/( psi(-q)* phi(-q^18)) in powers of q where phi(), psi(), chi() are Ramanujan theta functions.
A145727 Expansion of f(q) * f(q^15) / (f(-q^6) * f(-q^10)) in powers of q where f() is a Ramanujan theta function.
A145782 Expansion of (chi(q^3) * chi(q^5))^2 / (chi(q) * chi(q^15)) in powers of q where chi() is a Ramanujan theta function.

A093829 A113661 A113974 A122860    -->    4 -1 1 -4    (34)
A093829 Expansion of q * psi(q^3)^3 / psi(q) in powers of q where psi() is a Ramanujan theta function.
A113661 Expansion of (phi(x)^3/phi(x^3)-1)/6 where phi() is a Ramanujan theta function.
A113974 Expansion of (1-phi(x^3)^3/phi(x))/2 where phi() is a Ramanujan theta function.
A122860 Expansion of (1 - phi(-q)^3 / phi(-q^3)) / 6 in powers of q where phi() is a Ramanujan theta function.

Best regards,


-- 
Thomas Baruchel