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Search: id:A144617
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| A144617 |
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Triangle read by rows: numerators of coefficients of the Debye-type polynomial u_n used for asymptotic Airy-type expansions of Bessel functions of arbitrary large order. |
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+0
2
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| 1, 3, -5, 81, -462, 385, 30375, -369603, 765765, -425425, 4465125, -94121676, 349922430, -446185740, 185910725, 1519035525, -49286948607, 284499769554, -614135872350, 566098157625, -188699385875
(list; table; graph; listen)
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OFFSET
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0,2
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LINKS
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Chris Kormanyos, Rows n=0..121 of triangle, flattened
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972. See Section 9.3.9.
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. See Section 9.3.9.
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EXAMPLE
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The polynomials u_0, u_1, u_2 and u_3 are:
1
(3 t - 5 t^3)/24
(81 t^2 - 462 t^4 + 385 t^6)/1152
(30375 t^3 - 369603 t^5 + 765765 t^7 - 425425 t^9)/414720
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MATHEMATICA
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uktop = {1, 3, -5}; ukbot = {1, 24}; u = ((3 t) - (5 (t^3)))/24; Do[uk = (((1/2) (t^2) (1 - (t^2))) D[u, t]) + ((1/8) Integrate[((1 - (5 (t^2))) u), {t, 0, t}]); u = Simplify[uk]; Do[uktop = Append[uktop, Coefficient[Expand[Numerator[u]], t^n]], {n, k, 3 k, 2}]; ukbot = Append[ukbot, Denominator[u]]; Print[k], {k, 2, 8}]; [From Chris Kormanyos (ckormanyos(AT)yahoo.com), Jan 18 2009]
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CROSSREFS
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For denominators see A144618. Cf. A144622.
Sequence in context: A145616 A122912 A062214 this_sequence A107655 A133660 A057663
Adjacent sequences: A144614 A144615 A144616 this_sequence A144618 A144619 A144620
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KEYWORD
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sign,frac,tabl
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jan 15 2009, based on email from Chris Kormanyos (ckormanyos(AT)yahoo.com)
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EXTENSIONS
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Added terms up to u_5 Chris Kormanyos (ckormanyos(AT)yahoo.com), Jan 18 2009
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