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Search: id:A108214
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| A108214 |
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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. |
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+0
1
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| 8, 48, 576, 11520, 345600, 14515200, 812851200, 58525286400, 5267275776000, 579400335360000, 76480844267520000, 11931011705733120000, 2171444130443427840000, 456003267393119846400000
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OFFSET
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2,1
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COMMENT
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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?
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REFERENCES
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N. N. Lebedev & Richard A. Silverman (translator), Special Functions & their Applications, Dover Publications, New York, 1972, pp. 96-97.
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FORMULA
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a(n)=4(n-1)!n!
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MATHEMATICA
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Table[4(n-1)!(n)!, {n, 2, 16}] (* for the first 14 terms *)
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CROSSREFS
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Adjacent sequences: A108211 A108212 A108213 this_sequence A108215 A108216 A108217
Sequence in context: A013186 A072169 A052575 this_sequence A010568 A080493 A018200
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KEYWORD
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frac,easy,nonn
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AUTHOR
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Graham L. Giller (graham(AT)gillerinvestments.com), Jun 16 2005
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