[seqfan] person needing help with sequences
N. J. A. Sloane
njas at research.att.com
Sat Aug 14 18:11:59 CEST 2010
Dear Seq Fans, I received a request for
assistance - would anyone like to help him?
There were 2 emails:
Date: Fri, 13 Aug 2010 13:04:54 +0200
Subject: can you help me, please
From: Mohamed Jalel Atia <jalel.atia at gmail.com>
Can you help me with this, please:
I found the following integer sequences and I would like to ask you if meet
them:
1,15,49,6435,1571191,...
0,4,12,1624,390680,...
1,7,25,3187,789831,...
and later
Subject: Re: can you help me, please
From: Mohamed Jalel Atia <jalel.atia at gmail.com>
To: njas at research.att.com
Dear Prof. Sloane,
These sequences come from the recurrence coefficients of a polynomial
sequence P_n Orthogonal on [-1,1] with respect to the weight function
w(x)=\abs(x-1/2)/\sqrt (1-x)+ \abs(x+1/2)/\sqrt (1+x),
P_n fulfill
P_0=1, P_1=x,
P_{n+2}=xP_{n+1}-\gamma_{n+1}P_n, n\geq 0,
whrer
\gamma_1=1/2
\gamma_2=1/4
\gamma_3=7/30
\gamma_4=4/15
\gamma_5=1/4
\gamma_6=12/49
\gamma_7=25/98
\gamma_8=1/4
\gamma_9=3187/12870
\gamma_10=1624/6435
\gamma_11=1/4
\gamma_12=390680/1571191
in such a way that
\gamma_3+\gamma_4=1/2
\gamma_6+\gamma_7=1/2
\gamma_9+\gamma_10=1/2
etc....
Thank you very much,
Mohamed Jalel Atia.
Neil
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