D. H. Bailey and J. M. Borwein, High-precision numerical integration: Progress and challenges, Journal of Symbolic Computation, vol.46, issue.7, pp.741-754, 2011.

D. H. Bailey, H. Yozo, X. S. Li, and B. Thompson, ARPREC: An arbitrary precision computation package, 2002.

I. Bogaert, Iteration-Free Computation of Gauss--Legendre Quadrature Nodes and Weights, SIAM Journal on Scientific Computing, vol.36, issue.3, pp.1008-1026, 2014.
DOI : 10.1137/140954969

I. Bogaert, B. Michiels, and J. Fostier, $\mathcal{O}(1)$ Computation of Legendre Polynomials and Gauss--Legendre Nodes and Weights for Parallel Computing, SIAM Journal on Scientific Computing, vol.34, issue.3, pp.83-101, 2012.
DOI : 10.1137/110855442

R. P. Brent, Asymptotic approximation of central binomial coefficients with rigorous error bounds, 2016.

Y. Chow, L. Gatteschi, and R. Wong, A Bernstein-type inequality for the Jacobi polynomial, Proceedings of the American Mathematical Society, vol.121, issue.3, pp.703-709, 1994.

D. V. Chudnovsky and G. V. Chudnovsky, Computer algebra in the service of mathematical physics and number theory, Computers in Talks from the International Conference on Computers and Mathematics, pp.109-232, 1986.

L. Fousse, Accurate Multiple-Precision Gauss-Legendre Quadrature, 18th IEEE Symposium on Computer Arithmetic (ARITH '07), pp.150-160, 2007.

G. H. Golub and J. H. Welsch, Calculation of Gauss quadrature rules, Mathematics of Computation, vol.23, issue.106, pp.221-230, 1969.

T. Granlund, G. Development-team, and . Mp, The GNU Multiple Precision Arithmetic Library

N. Hale and A. Townsend, Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights, SIAM Journal on Scientific Computing, vol.35, issue.2, pp.652-674, 2013.
DOI : 10.1137/120889873

F. Johansson, Evaluating parametric holonomic sequences using rectangular splitting, Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation, ISSAC '14, pp.256-263

F. Johansson, Efficient Implementation of Elementary Functions in the Medium-Precision Range, 2015 IEEE 22nd Symposium on Computer Arithmetic, pp.83-89, 2015.

F. Johansson, Computing hypergeometric functions rigorously, 2016.

F. Johansson, Arb: Efficient Arbitrary-Precision Midpoint-Radius Interval Arithmetic, IEEE Transactions on Computers, vol.66, issue.8, pp.1281-1292, 2017.

A. Kobel and M. Sagraloff, Fast approximate polynomial multipoint evaluation and applications , arXiv preprint, 2013.

M. A. Kowalski, A. G. Werschulz, and H. Wo?niakowski, Is Gauss quadrature optimal for analytic functions?, Numerische Mathematik, vol.8, issue.1, pp.47-89, 1985.
DOI : 10.1090/coll/023

R. E. Moore, Methods and applications of interval analysis, SIAM, 1979.

F. W. Olver, Asymptotics and Special Functions, A K Peters, 1997.

K. Petras, On the computation of the Gauss???Legendre quadrature formula with a given precision, Journal of Computational and Applied Mathematics, vol.112, issue.1-2, pp.253-267, 1999.

K. Petras, Self-validating integration and approximation of piecewise analytic functions, Journal of Computational and Applied Mathematics, vol.145, issue.2, pp.345-359, 2002.

D. M. Smith, Efficient multiple-precision evaluation of elementary functions, Mathematics of Computation, vol.52, issue.185, pp.131-134, 1989.

H. Takahasi and M. Mori, Double exponential formulas for numerical integration, Publications of the Research Institute for Mathematical Sciences, vol.9, issue.3, pp.721-741, 1974.

A. Townsend, The race for high order Gauss?Legendre quadrature, SIAM News, pp.1-3, 2015.

L. N. Trefethen, Is Gauss quadrature better than Clenshaw?Curtis?, SIAM review, pp.67-87, 2008.

J. Wimp, Computation with Recurrence Relations, 1984.