DLMF: Bibliography N ‣ Bibliography (original) (raw)

• Numerical Algorithms Group, Ltd..

• A. Nakamura (1996) Toda equation and its solutions in special functions. J. Phys. Soc. Japan 65 (6), pp. 1589–1597.

• 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. Software 18 (3), pp. 345–349.

• 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.

• W. Narkiewicz (2000) The Development of Prime Number Theory: From Euclid to Hardy and Littlewood. Springer-Verlag, Berlin.

• A. Natarajan and N. Mohankumar (1993) On the numerical evaluation of the generalised Fermi-Dirac integrals. Comput. Phys. Comm. 76 (1), pp. 48–50.

• National Bureau of Standards (1944) Tables of Lagrangian Interpolation Coefficients. Columbia University Press, New York.

• National Physical Laboratory (1961) Modern Computing Methods. 2nd edition, Notes on Applied Science, No. 16, Her Majesty’s Stationery Office, London.

• L. M. Navas, F. J. Ruiz, and J. L. Varona (2013) Asymptotic behavior of the Lerch transcendent function. J. Approx. Theory 170, pp. 21–31.

• D. Naylor (1984) On simplified asymptotic formulas for a class of Mathieu functions. SIAM J. Math. Anal. 15 (6), pp. 1205–1213.

• D. Naylor (1987) On a simplified asymptotic formula for the Mathieu function of the third kind. SIAM J. Math. Anal. 18 (6), pp. 1616–1629.

• D. Naylor (1989) On an integral transform involving a class of Mathieu functions. SIAM J. Math. Anal. 20 (6), pp. 1500–1513.

• D. Naylor (1990) On an asymptotic expansion of the Kontorovich-Lebedev transform. Applicable Anal. 39 (4), pp. 249–263.

• D. Naylor (1996) On an asymptotic expansion of the Kontorovich-Lebedev transform. Methods Appl. Anal. 3 (1), pp. 98–108.

• 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.

• M. Neher (2007) Complex standard functions and their implementation in the CoStLy library. ACM Trans. Math. Softw. 33 (1), pp. Article 2.

• W. J. Nellis and B. C. Carlson (1966) Reduction and evaluation of elliptic integrals. Math. Comp. 20 (94), pp. 223–231.

• G. Nemes (2017a) Error bounds for the asymptotic expansion of the Hurwitz zeta function. Proc. A. 473 (2203), pp. 20170363, 16.

• 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 (2013a) An explicit formula for the coefficients in Laplace’s method. Constr. Approx. 38 (3), pp. 471–487.

• 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 (2013c) Generalization of Binet’s Gamma function formulas. Integral Transforms Spec. Funct. 24 (8), pp. 597–606.

• G. Nemes (2014a) Error bounds and exponential improvement for the asymptotic expansion of the Barnes G-function. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 470 (2172), pp. 20140534, 14.

• G. Nemes (2014b) The resurgence properties of the large order asymptotics of the Anger-Weber function I. J. Class. Anal. 4 (1), pp. 1–39.

• G. Nemes (2014c) The resurgence properties of the large order asymptotics of the Anger-Weber function II. J. Class. Anal. 4 (2), pp. 121–147.

• G. Nemes (2015a) Error bounds and exponential improvements for the asymptotic expansions of the gamma function and its reciprocal. Proc. Roy. Soc. Edinburgh Sect. A 145 (3), pp. 571–596.

• G. Nemes (2015b) On the large argument asymptotics of the Lommel function via Stieltjes transforms. Asymptot. Anal. 91 (3-4), pp. 265–281.

• G. Nemes (2015c) The resurgence properties of the incomplete gamma function II. Stud. Appl. Math. 135 (1), pp. 86–116.

• G. Nemes (2016) The resurgence properties of the incomplete gamma function, I. Anal. Appl. (Singap.) 14 (5), pp. 631–677.

• G. Nemes (2017b) Error Bounds for the Large-Argument Asymptotic Expansions of the Hankel and Bessel Functions. Acta Appl. Math. 150, pp. 141–177.

• G. Nemes (2018) Error bounds for the large-argument asymptotic expansions of the Lommel and allied functions. Stud. Appl. Math. 140 (4), pp. 508–541.

• G. Nemes (2020) An extension of Laplace’s method. Constr. Approx. 51 (2), pp. 247–272.

• G. Nemes (2021) Proofs of two conjectures on the real zeros of the cylinder and Airy functions. SIAM J. Math. Anal. 53 (4), pp. 4328–4349.

• G. Németh (1992) Mathematical Approximation of Special Functions. Nova Science Publishers Inc., Commack, NY.

• 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.

• NetNUMPAC (free Fortran library)

• E. Neuman (1969a) Elliptic integrals of the second and third kinds. Zastos. Mat. 11, pp. 99–102.

• E. Neuman (1969b) On the calculation of elliptic integrals of the second and third kinds. Zastos. Mat. 11, pp. 91–94.

• E. Neuman (2003) Bounds for symmetric elliptic integrals. J. Approx. Theory 122 (2), pp. 249–259.

• 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).

• E. Neuman (2013) Inequalities and bounds for the incomplete gamma function. Results Math. 63 (3-4), pp. 1209–1214.

• P. G. Nevai (1979) Orthogonal polynomials. Mem. Amer. Math. Soc. 18 (213), pp. v+185 pp..

• P. Nevai (1986) Géza Freud, orthogonal polynomials and Christoffel functions. A case study. J. Approx. Theory 48 (1), pp. 3–167.

• E. H. Neville (1951) Jacobian Elliptic Functions. 2nd edition, Clarendon Press, Oxford.

• J. N. Newman (1984) Approximations for the Bessel and Struve functions. Math. Comp. 43 (168), pp. 551–556.

• M. Newman (1967) Solving equations exactly. J. Res. Nat. Bur. Standards Sect. B 71B, pp. 171–179.

• R. G. Newton (2002) Scattering theory of waves and particles. Dover Publications, Inc., Mineola, NY.

• T. D. Newton (1952) Coulomb Functions for Large Values of the Parameter η. Technical report Atomic Energy of Canada Limited, Chalk River, Ontario.

• E. W. Ng and M. Geller (1969) A table of integrals of the error functions. J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.

• N. Nielsen (1906a) Handbuch der Theorie der Gammafunktion. B. G. Teubner, Leipzig (German).

• N. Nielsen (1906b) Theorie des Integrallogarithmus und verwandter Transzendenten. B. G. Teubner, Leipzig (German).

• N. Nielsen (1909) Der Eulersche Dilogarithmus und seine Verallgemeinerungen. Nova Acta Leopoldina 90, pp. 123–212.

• N. Nielsen (1923) Traité Élémentaire des Nombres de Bernoulli. Gauthier-Villars, Paris.

• 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).

• 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.

• Y. Nievergelt (1995) Bisection hardly ever converges linearly. Numer. Math. 70 (1), pp. 111–118.

• A. Nijenhuis and H. S. Wilf (1975) Combinatorial Algorithms. Academic Press, New York.

• A. F. Nikiforov and V. B. Uvarov (1988) Special Functions of Mathematical Physics: A Unified Introduction with Applications. Birkhäuser Verlag, Basel.

• G. Nikolov and V. Pillwein (2015) An extension of Turán’s inequality. Math. Inequal. Appl. 18 (1), pp. 321–335.

• I. Niven, H. S. Zuckerman, and H. L. Montgomery (1991) An Introduction to the Theory of Numbers. 5th edition, John Wiley & Sons Inc., New York.

• NMS (free collection of Fortran subroutines)

• C. J. Noble and I. J. Thompson (1984) COULN, a program for evaluating negative energy Coulomb functions. Comput. Phys. Comm. 33 (4), pp. 413–419.

• C. J. Noble (2004) Evaluation of negative energy Coulomb (Whittaker) functions. Comput. Phys. Comm. 159 (1), pp. 55–62.

• V. A. Noonburg (1995) A separating surface for the Painlevé differential equation x′′=x2−t. J. Math. Anal. Appl. 193 (3), pp. 817–831.

• N. E. Nørlund (1955) Hypergeometric functions. Acta Math. 94, pp. 289–349.

• N. E. Nörlund (1922) Mémoire sur les polynomes de Bernoulli. Acta Math. 43, pp. 121–196 (French).

• N. E. Nörlund (1924) Vorlesungen über Differenzenrechnung. Springer-Verlag, Berlin (German).

• L. N. Nosova and S. A. Tumarkin (1965) Tables of Generalized Airy Functions for the Asymptotic Solution of the Differential Equations ϵ⁢(p⁢y′)′+(q+ϵ⁢r)⁢y=f. 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.

• M. Noumi and Y. Yamada (1998) Affine Weyl groups, discrete dynamical systems and Painlevé equations. Comm. Math. Phys. 199 (2), pp. 281–295.

• M. Noumi and Y. Yamada (1999) Symmetries in the fourth Painlevé equation and Okamoto polynomials. Nagoya Math. J. 153, pp. 53–86.

• M. Noumi (2004) Painlevé Equations through Symmetry. Translations of Mathematical Monographs, Vol. 223, American Mathematical Society, Providence, RI.

• V. Yu. Novokshënov (1985) The asymptotic behavior of the general real solution of the third Painlevé equation. Dokl. Akad. Nauk SSSR 283 (5), pp. 1161–1165 (Russian).

• 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).

• Number Theory Web (website)

• Numerical Recipes (commercial C, C++, Fortran 77, and Fortran 90 libraries)

• H. M. Nussenzveig (1965) High-frequency scattering by an impenetrable sphere. Ann. Physics 34 (1), pp. 23–95.

• H. M. Nussenzveig (1992) Diffraction Effects in Semiclassical Scattering. Montroll Memorial Lecture Series in Mathematical Physics, Cambridge University Press.

• J. F. Nye (1999) Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations. Institute of Physics Publishing, Bristol.

• J. F. Nye (2006) Dislocation lines in the hyperbolic umbilic diffraction catastrophe. Proc. Roy. Soc. Lond. Ser. A 462, pp. 2299–2313.

• J. F. Nye (2007) Dislocation lines in the swallowtail diffraction catastrophe. Proc. Roy. Soc. Lond. Ser. A 463, pp. 343–355.