lauricella function

Lauricella $D$-Hypergeometric Function

Computes the Lauricella $D$-hypergeometric function.

lauricella(a, b, g, x, eps = 1e-06)

Arguments

• a: numeric.
• b: numeric vector.
• g: numeric.
• x: numeric vector. x must have the same length as b.
• eps: numeric. Precision for the nested sums (default 1e-06).

Returns

A numeric value: the value of the Lauricella function, with two attributes attr(, "epsilon") (precision of the result) and attr(, "k") (number of iterations).

Details

If $n$ is the length of the $b$ and x vectors, the Lauricella $D$-hypergeometric function is given by:

where $(x)_p$ is the Pochhammer symbol (see pochhammer).

If $|x_i| < 1, i = 1, \dots, n$, this sum converges. Otherwise there is an error.

The eps argument gives the required precision for its computation. It is the attr(, "epsilon") attribute of the returned value.

References

N. Bouhlel, A. Dziri, Kullback-Leibler Divergence Between Multivariate Generalized Gaussian Distributions. IEEE Signal Processing Letters, vol. 26 no. 7, July 2019. tools:::Rd_expr_doi("10.1109/LSP.2019.2915000")

N. Bouhlel and D. Rousseau (2023), Exact Rényi and Kullback-Leibler Divergences Between Multivariate t-Distributions. IEEE Signal Processing Letters, vol. 30, pp. 1672-1676, October 2023. tools:::Rd_expr_doi("10.1109/LSP.2023.3324594")

Author(s)

Pierre Santagostini, Nizar Bouhlel