|
|
A108214
|
|
Denominator of the O(x^2) term in the Maclaurin series of the square of the Jacobi polynomial P^{a,b}_n(z) about z=1-x for real positive x.
|
|
0
|
|
|
8, 48, 576, 11520, 345600, 14515200, 812851200, 58525286400, 5267275776000, 579400335360000, 76480844267520000, 11931011705733120000, 2171444130443427840000, 456003267393119846400000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
2,1
|
|
COMMENTS
|
The sequence starts at n=2 because the n=1 and n=0 terms are not quadratic in x and the denominator of 0 is undefined.
This sequence arises out of my preliminary investigation into the square-summability of the Jacobi polynomials, i.e., does Sum_{n=0}^ infinity {P^{a,b}_n(z)}^2 exist?
|
|
REFERENCES
|
N. N. Lebedev & Richard A. Silverman (translator), Special Functions & their Applications, Dover Publications, New York, 1972, pp. 96-97.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 4*(n-1)!*n!.
|
|
MATHEMATICA
|
Table[4(n-1)!(n)!, {n, 2, 16}] (* for the first 14 terms *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
frac,easy,nonn
|
|
AUTHOR
|
Graham L. Giller (graham(AT)gillerinvestments.com), Jun 16 2005
|
|
STATUS
|
approved
|
|
|
|