[seqfan] Re: A299434 / A299435 = A005447 / A005446 ?
Paul Hanna
pauldhanna.math at gmail.com
Sat Feb 10 12:55:08 CET 2018
Thanks, Robert, for the confirmation.
I'll recycle the new A-numbers, and add Cf. to the existing A-numbers
A005447 / A005446
to point to related new sequences A299430 / A299431 (C(x)) and A299432 /
A299433 (S(x)).
Thank you,
Paul
On Fri, Feb 9, 2018 at 7:51 PM, <israel at math.ubc.ca> wrote:
> Yes, A299434 is the same as A005447, and A299432 is the same as A005446.
> The differential equation for y = C(x)^(1/2) in A299434 is y' = x y/(y -
> 1), and
> y=-W_{-1}(-e^{-1-x^2/2}) is a solution of this.
> The sequences should be merged.
>
> Cheers,
> Robert
>
> February 9, 2018 3:23 PM, "Paul Hanna" <pauldhanna.math at gmail.com> wrote:
>
> > SeqFans,
> > Are the following sequences essentially the same?
> >
> > https://oeis.org/A299434 = https://oeis.org/A005447 ?
> > https://oeis.org/A299435 = https://oeis.org/A005446 ?
> >
> > If so, then some formulas could be added to the following sequences as
> > well:
> >
> > A299430 / A299431 = coefficients in C(x)
> > A299432 / A299433 = coefficients in S(x)
> >
> > These sequences describe the power series C(x) and S(x) that satisfy:
> >
> > C(x)^(1/2) - S(x)^(1/2) = 1
> >
> > analogous to the hyperbolic cosine, sine functions.
> >
> > Thanks,
> > Paul
> >
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>
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