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An algorithm for the evaluation of the complex Airy functions. (English) Zbl 0401.65010

65D20Computation of special functions, construction of tables
65D32Quadrature and cubature formulas (numerical methods)
33C10Bessel and Airy functions, cylinder functions, ${}_0F_1$
Full Text: DOI
[1] Abramowitz, M.; Stegun, I. A.: Handbook of mathematical functions. (1970) · Zbl 0171.38503
[2] Carrier, G. F.; Krook, M.; Pearson, C. E.: Functions of a complex variable. (1966) · Zbl 0146.29801
[3] Child, M. S.: Molecular phys.. 28, 495 (1974)
[4] Gradshetyn, I. S.; Ryzhik, I. M.: Tables of integrals, series, and products. (1965)
[5] Ibid., Formula 6.621.3.
[6] Gordon, R. G.: Methods. comput. Phys.. 10, 81 (1971)
[7] Gordon, R. G.: J. math. Phys.. 9, 1087 (1968)
[8] Latham, W. P.; Redding, R. W.: J. computational phys.. 16, 66 (1974)
[9] Luthey, Z. A.: Piecewise analytical solution method for the radial schroedinger equation. Thesis (1974)
[10] Miller, J. C. P.: The Airy integral. British assoc. Adv. sci., mathematical tables (1946) · Zbl 0061.30506
[11] Muskhelishvili, N. I.: Singular integral equations. (1953) · Zbl 0051.33203
[12] Olver, F. W. J.: Philos. trans. Roy. soc. London ser A. 247, 328 (1954)
[13] Olver, F. W. J.: Philos. trans. Roy. soc, London ser. A. 278, 137 (1975)
[14] Olver, F. W. J.: Asymptotics and special functions. (1974) · Zbl 0303.41035
[15] Prince, P. J.: ACM trans. Math. softw.. 1, 372 (1975)
[16] M. Shapiro and B. Gerber, Dept. Chem. Phys., Weizmann Institute, Rehovot, Israel, private communication.
[17] Shohat, J. A.; Tamarkin, J. D.: The problem of moments. (1943) · Zbl 0063.06973
[18] Woodward, P. M.; Woodward, A. M.; Heusman, R.; Davies, H. H.; Gamble, N.: Philos. mag.. 37, 236 (1946)