[seqfan] Re: Zeros in A172390 and A172391
Paul D Hanna
pauldhanna at juno.com
Mon Mar 29 23:56:12 CEST 2010
SeqFans,
Just realized that the statements in the prior emails reduce to the following.
Let
A(x) = g.f. of A172390, and
B(x) = g.f. of A172391;
then
A(x)^(1/2) = F(x^2) + 4x/F(x^2) and
B(x)^(1/2) = G(x^2) + 4x/G(x^2).
This statement seems significant ... what does it imply about A172390 and A172391?
All the statements in the prior emails are simple deductions from the above -
so sorry for the email clutter!!
Paul
---------- Original Message ----------
From: "Paul D Hanna" <pauldhanna at juno.com>
To: seqfan at list.seqfan.eu
Subject: [seqfan] Re: Zeros in A172390 and A172391
Date: Mon, 29 Mar 2010 21:06:44 GMT
SeqFans,
To expand on Joerg's observation,
here is a relation that both sequences A172390 and A172391 seem to have in common.
No doubt the relation is due to their elliptic connections.
Let
A(x) = g.f. of A172390, and
B(x) = g.f. of A172391;
then the following functions equal the sum of the respective quadrasections defined by:
sqrt( sqrt(A(x^2)) + 4*x ) = QA0(x^4) + x*QA1(x^4)
sqrt( sqrt(B(x^2)) + 4*x ) = QB0(x^4) + x*QB1(x^4)
such that the quadrasections satisfy the product:
QA0(x^4)*QA1(x^4) = QB0(x^4)*QB1(x^4) = 2
and also
QA0(x^2)^2 + x*QA1(x^2)^2 = sqrt(A(x)) ;
QB0(x^2)^2 + x*QB1(x^2)^2 = sqrt(B(x)).
Please see examples below.
Is this relation trivial?
Paul
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