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A211268 Integral of a Gaussian peak with unit height and unit half-height width. 1
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 half-height 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 sinc-type 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 half-height 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

Table of n, a(n) for n=1..105.

FORMULA

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

EXAMPLE

1.064467019431226179315267

CROSSREFS

Cf. A211269 (for sinc-shaped peaks).

Cf. A019669 (for Lorentzian-shaped peaks).

Sequence in context: A201285 A195359 A198840 * A021612 A201587 A110756

Adjacent sequences:  A211265 A211266 A211267 * A211269 A211270 A211271

KEYWORD

nonn,cons,easy

AUTHOR

Stanislav Sykora, Apr 07 2012

STATUS

approved

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Last modified March 24 06:12 EDT 2017. Contains 283984 sequences.