The NAG Libraries are large general purpose numerical software libraries
with broad coverage of elementary and special functions.
Implementations are in single and double precision.
M. Nardin, W. F. Perger, and A. Bhalla (1992a)Algorithm 707: CONHYP: A numerical evaluator of the confluent hypergeometric function for complex arguments of large magnitudes.
ACM Trans. Math. Software18 (3), pp. 345–349.
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Notes:
Double-precision Fortran, minimum accuracy 9S,
maximum accuracy 13S.
M. Nardin, W. F. Perger, and A. Bhalla (1992b)Numerical evaluation of the confluent hypergeometric function for complex arguments of large magnitudes.
J. Comput. Appl. Math.39 (2), pp. 193–200.
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Notes:
Extended-precision Fortran evaluator, minimum accuracy 9S,
maximum accuracy 13S.
National Bureau of Standards (1958)Integrals of Airy Functions.
National Bureau of Standards Applied Mathematics Series, U.S. Government Printing Office, Washington, D.C..
National Bureau of Standards (1967)Tables Relating to Mathieu Functions: Characteristic Values, Coefficients, and Joining Factors.
2nd edition, National Bureau of Standards Applied Mathematics Series, U.S. Government Printing Office, Washington, D.C..
J. Negro, L. M. Nieto, and O. Rosas-Ortiz (2000)Confluent hypergeometric equations and related solvable potentials in quantum mechanics.
J. Math. Phys.41 (12), pp. 7964–7996.
G. Nemes and A. B. Olde Daalhuis (2016)Uniform asymptotic expansion for the incomplete beta function.
SIGMA Symmetry Integrability Geom. Methods Appl.12, pp. 101, 5 pages.
G. Nemes (2013b)Error bounds and exponential improvement for Hermite’s asymptotic expansion for the gamma function.
Appl. Anal. Discrete Math.7 (1), pp. 161–179.
G. Nemes (2014a)Error bounds and exponential improvement for the asymptotic expansion of the Barnes -function.
Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.470 (2172), pp. 20140534, 14.
G. Nemes (2015a)Error bounds and exponential improvements for the asymptotic expansions of the gamma function and its reciprocal.
Proc. Roy. Soc. Edinburgh Sect. A145 (3), pp. 571–596.
J. J. Nestor (1984)Uniform Asymptotic Approximations of Solutions of Second-order Linear Differential Equations, with a Coalescing Simple Turning Point and Simple Pole.
Ph.D. Thesis, University of Maryland, College Park, MD.
E. Neuman (2004)Inequalities involving Bessel functions of the first kind.
JIPAM. J. Inequal. Pure Appl. Math.5 (4), pp. Article 94, 4 pp. (electronic).
N. Nielsen (1965)Die Gammafunktion. Band I. Handbuch der Theorie der Gammafunktion. Band II. Theorie des Integrallogarithmus und verwandter Transzendenten.
Chelsea Publishing Co., New York (German).
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Notes:
Both books are textually unaltered except for correction of errata.
M. M. Nieto and L. M. Simmons (1979)Eigenstates, coherent states, and uncertainty products for the Morse oscillator.
Phys. Rev. A (3)19 (2), pp. 438–444.
L. N. Nosova and S. A. Tumarkin (1965)Tables of Generalized Airy Functions for the Asymptotic Solution of the Differential Equations .
Pergamon Press, Oxford.
M. Noumi and J. V. Stokman (2004)Askey-Wilson polynomials: an affine Hecke algebra approach.
In Laredo Lectures on Orthogonal Polynomials and Special
Functions,
Adv. Theory Spec. Funct. Orthogonal Polynomials, pp. 111–144.
V. Yu. Novokshënov (1985)The asymptotic behavior of the general real solution of the third Painlevé equation.
Dokl. Akad. Nauk SSSR283 (5), pp. 1161–1165 (Russian).
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Notes:
In Russian. English translation: Sov. Math., Dokl.
30(1988), no. 8, pp. 666–668.
V. Yu. Novokshënov (1990)The Boutroux ansatz for the second Painlevé equation in the complex domain.
Izv. Akad. Nauk SSSR Ser. Mat.54 (6), pp. 1229–1251 (Russian).
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Notes:
In Russian. English translation: Math. USSR-Izv.
37(1991), no. 3, pp. 587–609.
H. M. Nussenzveig (1992)Diffraction Effects in Semiclassical Scattering.
Montroll Memorial Lecture Series in Mathematical Physics, Cambridge University Press.
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Notes:
Also available electronically through Cambridge Books Online, ISBN 9780511599903.