

A211268


Integral of a Gaussian peak with unit height and unit halfheight width.


2



1, 0, 6, 4, 4, 6, 7, 0, 1, 9, 4, 3, 1, 2, 2, 6, 1, 7, 9, 3, 1, 5, 2, 6, 7, 5, 9, 6, 2, 3, 4, 6, 2, 0, 1, 0, 6, 9, 4, 2, 9, 4, 3, 0, 9, 4, 2, 4, 1, 7, 2, 0, 2, 3, 2, 5, 3, 8, 5, 2, 4, 7, 7, 9, 2, 7, 3, 2, 6, 7, 4, 6, 0, 9, 6, 9, 4, 2, 3, 1, 3, 9, 1, 9, 2, 6, 1, 7, 5, 5, 4, 0, 2, 4, 2, 0, 7, 4, 4, 8, 1, 2, 6, 2, 8
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

In spectroscopy, when comparing absorbtion peak shapes, the functions are first scaled vertically and horizontally to a canonical form with unit height and unit halfheight width. The 4 most common canonical shapes are: rectangular R(x)=1 for x<=1/2 (0 otherwise), Lorentzian L(x)=1/(1+(2x)^2), Gaussian G(x)=exp(log(2)(2x)^2), and sinctype S(x) (see A211269). The areas A under such canonical peaks (integral from inf to +inf) are 1.0 for R(x), (Pi/2)=A019669 for L(x), this constant for G(x), and A211269 for S(x). For a generic peak with height H and halfheight width W belonging to the same canonical family, the area is A*H*W. Hence the practical importance of the constant A.


REFERENCES

M. Quack and F. Merckt, Editors, Handbook of High Resolution Spectroscopy, Wiley, 2011.


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000


FORMULA

Equals sqrt(Pi/(4*log(2))).


EXAMPLE

1.064467019431226179315267...


MATHEMATICA

RealDigits[Sqrt[Pi/(4*Log[2])], 10, 50][[1]] (* G. C. Greubel, Mar 30 2017 *)


PROG

(PARI) sqrt(Pi/(4*log(2))) \\ G. C. Greubel, Mar 30 2017


CROSSREFS

Cf. A211269 (for sincshaped peaks).
Cf. A019669 (for Lorentzianshaped peaks).
Sequence in context: A195359 A316162 A198840 * A021612 A201587 A110756
Adjacent sequences: A211265 A211266 A211267 * A211269 A211270 A211271


KEYWORD

nonn,cons,easy


AUTHOR

Stanislav Sykora, Apr 07 2012


STATUS

approved



