[seqfan] Re: A299434 / A299435 = A005447 / A005446 ?

israel at math.ubc.ca israel at math.ubc.ca
Sat Feb 10 01:51:12 CET 2018


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
> 
> --
> Seqfan Mailing list - http://list.seqfan.eu


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