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%I #18 Mar 31 2017 03:52:57
%S 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,
%T 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,
%U 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
%N Integral of a Gaussian peak with unit height and unit half-height width.
%C 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.
%D M. Quack and F. Merckt, Editors, Handbook of High Resolution Spectroscopy, Wiley, 2011.
%H G. C. Greubel, <a href="/A211268/b211268.txt">Table of n, a(n) for n = 1..10000</a>
%F Equals sqrt(Pi/(4*log(2))).
%e 1.064467019431226179315267...
%t RealDigits[Sqrt[Pi/(4*Log[2])], 10, 50][[1]] (* _G. C. Greubel_, Mar 30 2017 *)
%o (PARI) sqrt(Pi/(4*log(2))) \\ _G. C. Greubel_, Mar 30 2017
%Y Cf. A211269 (for sinc-shaped peaks).
%Y Cf. A019669 (for Lorentzian-shaped peaks).
%K nonn,cons,easy
%O 1,3
%A _Stanislav Sykora_, Apr 07 2012
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