@Article{Ratnanather:2014:AIM,
  author =       "J. Tilak Ratnanather and Jung H. Kim and Sirong Zhang and
		  Anthony M. J. Davis and Stephen K. Lucas",
  title =        "Algorithm 935: {IIPBF}, a {MATLAB} toolbox for
                  infinite integral of products of two {Bessel} functions",
  journal =      "{ACM} Transactions on Mathematical Software",
  volume  =      40,
  number  =      2,
  year    =      2014,
  month   =      feb,
  pages =        "14:1--14:12",
  url =          "http://doi.acm.org/10.1145/2508435",
  accepted =     "29 July 2013",
  abstract =     "
                  A \texttt{MATLAB} toolbox, \texttt{IIPBF}, for
                  calculating infinite integrals involving a product of two
                  Bessel functions $J_{a}(\rho x)J_{b}(\tau x), J_{a}(\rho
                  x)Y_{b}(\tau x)$ and $Y_{a}(\rho x)Y_{b}(\tau x)$, for
                  non-negative integers $a,b$, and a well behaved function
                  $f(x)$, is described. Based on the Lucas algorithm
                  previously developed for $J_{a}(\rho x)J_{b}(\tau
                  x)$ only, \texttt{IIPBF} recasts each product as
                  the sum of two functions whose oscillatory behavior
                  is exploited in the three step procedure of adaptive
                  integration, summation and extrapolation. The toolbox
                  uses customised \texttt{QUADPACK} and \texttt{IMSL}
                  functions from a \texttt{MATLAB} conversion of the
                  \texttt{SLATEC} library. In addition, \texttt{MATLAB}'s
                  own \texttt{quadgk} function for adaptive Gauss-Kronrod
                  quadrature results in a significant speed up compared
                  with the original algorithm. Usage of \texttt{IIPBF}
                  is described and eighteen test cases illustrate the
                  robustness of the toolbox; five additional ones are used
                  to compare \texttt{IIPBF} with the \texttt{BESSELINT}
                  code for rational and exponential forms of $f(x)$ with
                  $J_{a}(\rho x)J_{b}(\tau x)$. Reliability for a broad
                  range of values of $\rho$ and $\tau$ for the three
                  different product types as well as different orders in
                  one case is demonstrated. An electronic appendix provides
                  a novel derivation of formulae for  five cases.",
}