*** Ingredients of the Local-form CMB Bispectrum, alpha and beta ***
December 12, 2010: E.Komatsu
Refs: Komatsu & Spergel, PRD 63, 063002 (2001)
      Komatsu, Spergel & Wandelt, ApJ, 634, 14 (2005)

Here we provide a program for computing the ingredients of the local-form
CMB bispectrum, alpha(l,r) and beta(l,r), from the radiation transfer function
of temperature anisotropy, gT(l,k), calculated from the gTfast code (also
available in Cosmology Routine Library). Here, l is the multipole, k
is the wavenumber, and r is the comoving distance. 

For definition of gT(l,k), see Eq.(10) of Komatsu & Spergel (2001).

For definition of alpha(l,r) and beta(l,r), see Eq.(3) and Eq.(6) of
Komatsu, Spergel & Wandelt (2005), respectively:

alpha(l,r) = (2/pi) int k^2*[gTl(k)*jl(kr)] dk
beta(l,r)  = (2/pi) int k^2*[gTl(k)*jl(kr)]*P(k) dk

where P(k) is the power spectrum of Bardeen's curvature perturbation
during the matter era (without the transfer function), and jl(x) is 
the usual spherical Bessel function. [Note that alpha and beta are the 
same as b^NL and b^L of Komatsu & Spergel (2001), respectively.]


- To compile and use the  program, edit Makefile
and simply "./make"
- It will generate an executable called "compute_alphabeta"
- Run "./compute_alphabeta", which will generate a data file containing 
l, r, dr, alpha, and beta, with the filename of your choice.