A145646 Wavelength (in ångströms) of the series limit of the Hydrogen spectrum for main quantum number n.

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.

Links

Table of n, a(n) for n=1..13.

Wikipedia, Rydberg Formula.

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

Adjacent sequences: A145643 A145644 A145645 * A145647 A145648 A145649

Keyword

nonn,less

Author

Paul Curtz, Oct 15 2008

Extensions

Edited by R. J. Mathar, Oct 17 2008

Status

approved