Gil, Azmparo; Segura, Javier; Temme, Nico M. McMahon-type asymptotic expansions of the zeros of the Coulomb wave functions. arXiv:2402.14537 Preprint, arXiv:2402.14537 [math.CA] (2024). MSC: 41A60 33C15 65D20 BibTeX Cite \textit{A. Gil} et al., ``McMahon-type asymptotic expansions of the zeros of the Coulomb wave functions'', Preprint, arXiv:2402.14537 [math.CA] (2024) Full Text: arXiv OA License
Gil, Amparo; Segura, Javier; Temme, Nico M. New asymptotic representations of the noncentral \(t\)-distribution. (English) Zbl 07771123 Stud. Appl. Math. 151, No. 3, 857-882 (2023). MSC: 62-XX 33-XX PDFBibTeX XMLCite \textit{A. Gil} et al., Stud. Appl. Math. 151, No. 3, 857--882 (2023; Zbl 07771123) Full Text: DOI arXiv
Gil, Amparo; Odrzywołek, Andrzej; Segura, Javier; Temme, Nico M. Evaluation of the generalized Fermi-Dirac integral and its derivatives for moderate/large values of the parameters. (English) Zbl 07693413 Comput. Phys. Commun. 283, Article ID 108563, 9 p. (2023). MSC: 82-XX 68-XX PDFBibTeX XMLCite \textit{A. Gil} et al., Comput. Phys. Commun. 283, Article ID 108563, 9 p. (2023; Zbl 07693413) Full Text: DOI
Gil, A.; Segura, J.; Temme, N. M. A new asymptotic representation and inversion method for the Student’s \(t\) distribution. (English) Zbl 07566915 Integral Transforms Spec. Funct. 33, No. 8, 597-608 (2022). MSC: 65-XX 33B20 41A60 65D20 PDFBibTeX XMLCite \textit{A. Gil} et al., Integral Transforms Spec. Funct. 33, No. 8, 597--608 (2022; Zbl 07566915) Full Text: DOI arXiv
Gil, A.; Segura, J.; Temme, N. M. Complete asymptotic expansions for the relativistic Fermi-Dirac integral. (English) Zbl 1510.41013 Appl. Math. Comput. 412, Article ID 126618, 14 p. (2022). MSC: 41A60 33C15 65D15 PDFBibTeX XMLCite \textit{A. Gil} et al., Appl. Math. Comput. 412, Article ID 126618, 14 p. (2022; Zbl 1510.41013) Full Text: DOI arXiv
Segura, Javier Uniform (very) sharp bounds for ratios of parabolic cylinder functions. (English) Zbl 1493.33002 Stud. Appl. Math. 147, No. 2, 816-833 (2021). Reviewer: Francisco Pérez Acosta (La Laguna) MSC: 33C10 PDFBibTeX XMLCite \textit{J. Segura}, Stud. Appl. Math. 147, No. 2, 816--833 (2021; Zbl 1493.33002) Full Text: DOI arXiv
Gil, A.; Segura, J.; Temme, N. M. Asymptotic inversion of the binomial and negative binomial cumulative distribution functions. (English) Zbl 1450.33007 ETNA, Electron. Trans. Numer. Anal. 52, 270-280 (2020). MSC: 33B20 41A60 PDFBibTeX XMLCite \textit{A. Gil} et al., ETNA, Electron. Trans. Numer. Anal. 52, 270--280 (2020; Zbl 1450.33007) Full Text: DOI arXiv Link
Gil, A.; Segura, J.; Temme, N. M. Numerical evaluation of Airy-type integrals arising in uniform asymptotic analysis. (English) Zbl 1493.65045 J. Comput. Appl. Math. 371, Article ID 112717, 18 p. (2020). MSC: 65D20 33C10 41A60 65D32 PDFBibTeX XMLCite \textit{A. Gil} et al., J. Comput. Appl. Math. 371, Article ID 112717, 18 p. (2020; Zbl 1493.65045) Full Text: DOI arXiv Link
Gil, Amparo; Segura, Javier; Temme, Nico M. Noniterative computation of Gauss-Jacobi quadrature. (English) Zbl 1408.33020 SIAM J. Sci. Comput. 41, No. 1, A668-A693 (2019). MSC: 33C45 41A60 65D20 65D32 PDFBibTeX XMLCite \textit{A. Gil} et al., SIAM J. Sci. Comput. 41, No. 1, A668--A693 (2019; Zbl 1408.33020) Full Text: DOI arXiv
Gil, Amparo; Segura, Javier; Temme, Nico M. Asymptotic expansions of Jacobi polynomials for large values of \(\beta\) and of their zeros. (English) Zbl 1393.33011 SIGMA, Symmetry Integrability Geom. Methods Appl. 14, Paper 073, 9 p. (2018). MSC: 33C45 41A60 65D20 PDFBibTeX XMLCite \textit{A. Gil} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 14, Paper 073, 9 p. (2018; Zbl 1393.33011) Full Text: DOI arXiv
Gil, Amparo; Segura, Javier; Temme, Nico M. The asymptotic and numerical inversion of the Marcum \(Q\)-function. (English) Zbl 1302.33020 Stud. Appl. Math. 133, No. 2, 257-278 (2014). MSC: 33E20 33C10 65H05 PDFBibTeX XMLCite \textit{A. Gil} et al., Stud. Appl. Math. 133, No. 2, 257--278 (2014; Zbl 1302.33020) Full Text: DOI arXiv
Gil, Amparo; Segura, Javier; Temme, Nico M. Efficient and accurate algorithms for the computation and inversion of the incomplete gamma function ratios. (English) Zbl 1259.33006 SIAM J. Sci. Comput. 34, No. 6, A2965-A2981 (2012). MSC: 33B20 41A60 65D20 PDFBibTeX XMLCite \textit{A. Gil} et al., SIAM J. Sci. Comput. 34, No. 6, A2965--A2981 (2012; Zbl 1259.33006) Full Text: DOI arXiv Link
Gil, Amparo; Segura, Javier; Temme, Nico M. Basic methods for computing special functions. (English) Zbl 1216.65034 Simos, Theodore E. (ed.), Recent advances in computational and applied mathematics. Dordrecht: Springer (ISBN 978-90-481-9980-8/hbk; 978-90-481-9981-5/ebook). 67-121 (2011). MSC: 65D20 33C05 33C10 33C15 33F05 41A60 PDFBibTeX XMLCite \textit{A. Gil} et al., in: Recent advances in computational and applied mathematics. Dordrecht: Springer. 67--121 (2011; Zbl 1216.65034) Full Text: DOI Link
Gil, Amparo; Segura, Javier; Temme, Nico M. Computing the conical function \(P^{\mu}_{-1/2+i\tau}(x)\). (English) Zbl 1189.33006 SIAM J. Sci. Comput. 31, No. 3, 1716-1741 (2009). MSC: 33C05 33C10 41A60 65D20 PDFBibTeX XMLCite \textit{A. Gil} et al., SIAM J. Sci. Comput. 31, No. 3, 1716--1741 (2009; Zbl 1189.33006) Full Text: DOI
Deaño, Alfredo; Segura, Javier; Temme, Nico M. Identifying minimal and dominant solutions for Kummer recursions. (English) Zbl 1209.33004 Math. Comput. 77, No. 264, 2277-2293 (2008). Reviewer: Rajendra Kumar Yadav (Jodhpur) MSC: 33C15 39A10 41A60 65D20 PDFBibTeX XMLCite \textit{A. Deaño} et al., Math. Comput. 77, No. 264, 2277--2293 (2008; Zbl 1209.33004) Full Text: DOI
Gil, Amparo; Segura, Javier; Temme, Nico M. Numerically satisfactory solutions of hypergeometric recursions. (English) Zbl 1117.33005 Math. Comput. 76, No. 259, 1449-1468 (2007). Reviewer: Francisco Perez Acosta (La Laguna) MSC: 33C05 39A11 41A60 65D20 PDFBibTeX XMLCite \textit{A. Gil} et al., Math. Comput. 76, No. 259, 1449--1468 (2007; Zbl 1117.33005) Full Text: DOI
Gil, Amparo; Segura, Javier; Temme, Nico M. Computing complex Airy functions by numerical quadrature. (English) Zbl 1012.33001 Numer. Algorithms 30, No. 1, 11-23 (2002). Reviewer: Stamatis Koumandos (Nicosia) MSC: 33C10 33F05 41A60 30E10 65D20 65D32 PDFBibTeX XMLCite \textit{A. Gil} et al., Numer. Algorithms 30, No. 1, 11--23 (2002; Zbl 1012.33001) Full Text: DOI
Gil, Amparo; Segura, Javier; Temme, Nico M. On nonoscillating integrals for computing inhomogeneous Airy functions. (English) Zbl 0972.33004 Math. Comput. 70, No. 235, 1183-1194 (2001). Reviewer: N.M.Temme (Amsterdam) MSC: 33C10 41A60 30E10 65D20 PDFBibTeX XMLCite \textit{A. Gil} et al., Math. Comput. 70, No. 235, 1183--1194 (2001; Zbl 0972.33004) Full Text: DOI arXiv