Geodesic
McMahon-Type Asymptotic Expansions of the Zeros of the Coulomb Wave Functions
Symmetry, integrability and geometry: methods and applications, Tome 20 (2024) Cet article a éte moissonné depuis la source Math-Net.Ru

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We derive asymptotic expansions of the large zeros of the Coulomb wave functions and for those of their derivatives. The new expansions have the same form as the McMahon expansions of the zeros of the Bessel functions and reduce to them when a parameter is equal to zero. Numerical tests are provided to demonstrate the accuracy of the expansions.
Keywords: Coulomb wave functions, McMahon-type zeros, asymptotic expansions. 
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     title = {McMahon-Type {Asymptotic} {Expansions} of the {Zeros} of the {Coulomb} {Wave} {Functions}},
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Amparo Gil; Javier Segura; Nico M. Temme. McMahon-Type Asymptotic Expansions of the Zeros of the Coulomb Wave Functions. Symmetry, integrability and geometry: methods and applications, Tome 20 (2024). http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a74/

[1] Abramowitz M., “Asymptotic expansions of Coulomb wave functions”, Quart. Appl. Math., 7 (1949), 75–84 | DOI | MR | Zbl

[2] Ball J.S., “Automatic computation of zeros of Bessel functions and other special functions”, SIAM J. Sci. Comput., 21 (1999), 1458–1464 | DOI | MR

[3] Ikebe Y., “The zeros of regular Coulomb wave functions and of their derivatives”, Math. Comp., 29 (1975), 878–887 | DOI | MR | Zbl

[4] Luna B.K., Papenbrock T., “Low-energy bound states, resonances, and scattering of light ions”, Phys. Rev. C, 100 (2019), 054307, 17 pp., arXiv: 1907.11345 | DOI

[5] Mcmahon J., “On the roots of the Bessel and certain related functions”, Ann. of Math., 9 (1894), 23–30 | DOI | MR

[6] Miyazaki Y., Kikuchi Y., Cai D., Ikebe Y., “Error analysis for the computation of zeros of regular Coulomb wave function and its first derivative”, Math. Comp., 70 (2001), 1195–1204 | DOI | MR | Zbl

[7] Olver F.W.J., Maximon L.C., “Bessel functions”, NIST Handbook of Mathematical Functions, Cambridge University Press, Cambridge, 2010, 215–286 | MR

[8] Segura J., “Reliable computation of the zeros of solutions of second order linear ODEs using a fourth order method”, SIAM J. Numer. Anal., 48 (2010), 452–469 | DOI | MR | Zbl

[9] Temme N.M., Asymptotic methods for integrals, Ser. Anal., 6, World Scientific Publishing, Hackensack, NJ, 2014 | DOI | MR

[10] Thompson I.J., “Coulomb wave functions”, NIST Handbook of Mathematical Functions, Cambridge University Press, Cambridge, 2010, 741–756 | MR

[11] Watson G.N., A treatise on the theory of Bessel functions, Cambridge Math. Lib., 2nd ed., Cambridge University Press, Cambridge, 1944 | MR | Zbl