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A145646
Wavelength (in ångströms) of the series limit of the Hydrogen spectrum for main quantum number n.
2
911, 3645, 8201, 14580, 22782, 32806, 44652, 58321, 73813, 91127, 110263, 131222, 154004
OFFSET
1,1
COMMENTS
The series for n=1, 2, etc. are named after Lyman, Balmer, etc.
The sequence is ill-defined since it depends on the incompletely known natural constant A081821. Although the sequence is essentially proportional to n^2, rounding effects prevent high-term predictability of the differences. Taking relativistic corrections into account will worsen the situation. - R. J. Mathar, Oct 17 2008
REFERENCES
Robert Duane Cowan, The Theory of Atomic Structure and Spectra, Univ. California Press, 1981; in 3-7 Relativistic corrections.
FORMULA
a(n+1) - a(n) = A145647(n), first differences.
a(n) = round(n^2*10^10/A081821). - R. J. Mathar, Oct 17 2008
Conjectures from Colin Barker, May 07 2019: (Start)
G.f.: x*(911 + 912*x + 910*x^2 + 913*x^3 - x^4) / ((1 - x)^3*(1 + x^2)).
a(n) = (-1/8+i/8)*((3+3*i) + (-i)^n + i^(1+n) - (1+i)*n - (3645+3645*i)*n^2) where i=sqrt(-1).
a(n) = 3*a(n-1) - 4*a(n-2) + 4*a(n-3) - 3*a(n-4) + a(n-5) for n>5.
(End)
MAPLE
R := 10973731.568527 : for n from 1 to 13 do printf("%d, ", round(n^2*1.0e10/R) ); od; # R. J. Mathar, Oct 17 2008
CROSSREFS
Sequence in context: A210170 A068261 A119520 * A093634 A220984 A237084
KEYWORD
nonn,less
AUTHOR
Paul Curtz, Oct 15 2008
EXTENSIONS
Edited by R. J. Mathar, Oct 17 2008
STATUS
approved