@article{Ogata2005,
  title = {A {{Numerical Integration Formula Based}} on the {{Bessel Functions}}},
  volume = {41},
  abstract = {In this paper, we discuss the properties of a quadrature formula with the zeros of the Bessel functions as nodes for integrals  $\infty$ -$\infty$ | x | 2 $\nu$ +1 f ( x )d x, where $\nu$ is a real constant greater than - 1and f ( x ) is a function analytic on the real axis ( -$\infty$ , + $\infty$ ). We show from theoretical error analysis that (i) the quadrature formula converges exponentially, (ii) it is as accurate as the trapezoidal formula over ( -$\infty$ , + $\infty$ )and (iii) the accuracy of the quadrature formula doubles that of an interpolation formula with the same nodes. Numerical examples support the above theoretical results. We also apply the quadrature formula to the numerical integration of integral involving the Bessel function.},
  journal = {Publ RIMS Kyoto Univ},
  author = {Ogata, Hidenori},
  year = {2005},
  pages = {949-970},
  doi = {10.2977/prims/1145474602},
}
@article{Szapudi2005,
  title = {Fast {{Edge Corrected Measurement}} of the {{Two}}-{{Point Correlation Function}} and the {{Power Spectrum}}},
  doi = {10.1086/496971},
  abstract = {We present two related techniques to measure the two-point correlation function and the power spectrum with edge correction in any spatial dimensions. The underlying algorithm uses fast Fourier transforms for calculating the two-point function with an heuristically weighted edge corrected estimator. Once the correlation function is measured, we estimate the power spectrum via numerical integration of the Hankel transform connecting the two. We introduce an efficient numerical technique based on Gauss-Bessel-quadrature and double exponential transformation. This, combined with our, or any similar, two-point function estimator leads to a novel edge corrected estimator for power spectra. The pair of techniques presented are the Euclidean analogs of those developed and widely used in cosmic microwave background research for spherical maps.},
  journal = {Arxiv E-Prints},
  author = {Szapudi, Istv\'an and Pan, Jun and Prunet, Simon and Budav\'ari, Tam\'as},
  month = may,
  year = {2005},
  pages = {4-4},
  doi = {10.1086/496971}
}
@inbook{huybrechs_olver_2009,
  title = {Highly oscillatory quadrature},
  series = {London Mathematical Society Lecture Note Series},
  DOI = {10.1017/CBO9781139107136.003},
  booktitle = {Highly Oscillatory Problems},
  publisher = {Cambridge University Press},
  author = {Huybrechs, D. and Olver, S.},
  year={2009},
  pages={25–50},
  collection={London Mathematical Society Lecture Note Series}
}
@article{Ooura1999,
  title = {A Robust Double Exponential Formula for {{Fourier}}-Type Integrals},
  volume = {112},
  doi = {10.1016/S0377-0427(99)00223-X},
  abstract = {A double exponential transformation is presented to obtain a quadrature formula for Fourier-type integrals $\int$0$\infty$f(x)sin$\omega$xdx or $\int$0$\infty$f(x)cos$\omega$xdx where f(x) is a slowly decaying analytic function on (0,$\infty$). It is an improved version of what we previously proposed in 1991. The transformation x=$\varphi$(t) is such that it maps the interval (0,$\infty$) onto (-$\infty$,$\infty$), and that, while the integrand after the transformation decreases double exponentially at large negative t, the points of the formula approaches to zeros of sin$\omega$x or cos$\omega$x double exponentially at large positive t. Then the trapezoidal formula with an equal mesh size is applied to the integral over (-$\infty$,$\infty$) after the transformation, which gives an efficient quadrature formula for the Fourier-type integrals. The present transformation is improved in the sense that it can integrate a function f(z) with singularities in the finite z-plane more efficiently than the one previously proposed.},
  number = {1},
  journal = {Journal of Computational and Applied Mathematics},
  author = {Ooura, Takuya and Mori, Masatake},
  year = {1999},
  pages = {229-241}
}
@article{carton2001hydrodynamical,
  title={Hydrodynamical modeling of oceanic vortices},
  author={Carton, Xavier},
  journal={Surveys in Geophysics},
  volume={22},
  number={3},
  pages={179--263},
  year={2001},
  publisher={Springer}
}
