|
Search: id:A108214
|
|
|
| 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
1
|
|
| 8, 48, 576, 11520, 345600, 14515200, 812851200, 58525286400, 5267275776000, 579400335360000, 76480844267520000, 11931011705733120000, 2171444130443427840000, 456003267393119846400000
(list; graph; listen)
|
|
|
OFFSET
|
2,1
|
|
|
COMMENT
|
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}^ infty {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.
|
|
FORMULA
|
a(n)=4(n-1)!n!
|
|
MATHEMATICA
|
Table[4(n-1)!(n)!, {n, 2, 16}] (* for the first 14 terms *)
|
|
CROSSREFS
|
Sequence in context: A165748 A072169 A052575 this_sequence A010568 A080493 A018200
Adjacent sequences: A108211 A108212 A108213 this_sequence A108215 A108216 A108217
|
|
KEYWORD
|
frac,easy,nonn
|
|
AUTHOR
|
Graham L. Giller (graham(AT)gillerinvestments.com), Jun 16 2005
|
|
|
Search completed in 0.002 seconds
|
