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A211268
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Integral of a Gaussian peak with unit height and unit half-height width.
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2
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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
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OFFSET
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1,3
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COMMENTS
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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.
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REFERENCES
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M. Quack and F. Merckt, Editors, Handbook of High Resolution Spectroscopy, Wiley, 2011.
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LINKS
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FORMULA
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Equals sqrt(Pi/(4*log(2))).
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EXAMPLE
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1.064467019431226179315267...
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MATHEMATICA
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RealDigits[Sqrt[Pi/(4*Log[2])], 10, 50][[1]] (* G. C. Greubel, Mar 30 2017 *)
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PROG
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CROSSREFS
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Cf. A211269 (for sinc-shaped peaks).
Cf. A019669 (for Lorentzian-shaped peaks).
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KEYWORD
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AUTHOR
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STATUS
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approved
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