Bibliography N

♦A♦B♦C♦D♦E♦F♦G♦H♦I♦J♦K♦L♦M♦N♦O♦P♦Q♦R♦S♦T♦U♦V♦W♦X♦Y♦Z♦

NAG (commercial C and Fortran libraries)
Numerical Algorithms Group, Ltd..

Notes:

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.

Referenced by:

§ ‣ § Software Cross Index.

Encodings:

BibTeX
A. Nakamura (1996)
Toda equation and its solutions in special functions,

J. Phys. Soc. Japan 65 (6), pp. 1589–1597.

External Links:

ISSN 0031-9015, Document, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §18.38(ii).

Encodings:

BibTeX
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.

Notes:

Double-precision Fortran, minimum accuracy 9S, maximum accuracy 13S.

External Links:

ISSN 0098-3500, Document, TOMS module 707 (in GAMS), ZentralBlatt.

Referenced by:

§13.32(iii).

Encodings:

BibTeX
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.

Notes:

Extended-precision Fortran evaluator, minimum accuracy 9S, maximum accuracy 13S.

External Links:

ISSN 0377-0427, Document, MathReview Entry, ZentralBlatt.

Referenced by:

§13.32(iii).

Encodings:

BibTeX
W. Narkiewicz (2000)
The Development of Prime Number Theory: From Euclid to Hardy and Littlewood,

Springer-Verlag, Berlin.

External Links:

ISBN 3-540-66289-8, MathReview (D. R. Heath-Brown), ZentralBlatt.

Referenced by:

§27.12.

Encodings:

BibTeX
A. Natarajan and N. Mohankumar (1993)
On the numerical evaluation of the generalised Fermi-Dirac integrals,

Comput. Phys. Comm. 76 (1), pp. 48–50.

External Links:

ISSN 0010-4655, Document, ZentralBlatt.

Referenced by:

§25.18(i).

Encodings:

BibTeX
National Bureau of Standards (1944)
Tables of Lagrangian Interpolation Coefficients,

Columbia University Press, New York.

Notes:

Technical Director: Arnold N. Lowan

External Links:

MathReview (W. Feller), ZentralBlatt.

Referenced by:

§3.3(ii).

Encodings:

BibTeX
National Physical Laboratory (1961)
Modern Computing Methods,

2nd edition, Notes on Applied Science, No. 16, Her Majesty’s Stationery Office, London.

External Links:

MathReview (A. S. Householder), ZentralBlatt.

Referenced by:

§3.8(iv).

Encodings:

BibTeX
D. Naylor (1984)
On simplified asymptotic formulas for a class of Mathieu functions,

SIAM J. Math. Anal. 15 (6), pp. 1205–1213.

External Links:

ISSN 0036-1410, Document, MathReview (Harold Exton), ZentralBlatt.

Referenced by:

§28.26(ii).

Encodings:

BibTeX
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.

External Links:

ISSN 0036-1410, Document, MathReview (F. M. Arscott), ZentralBlatt.

Referenced by:

§28.26(ii).

Encodings:

BibTeX
D. Naylor (1989)
On an integral transform involving a class of Mathieu functions,

SIAM J. Math. Anal. 20 (6), pp. 1500–1513.

External Links:

ISSN 0036-1410, Document, MathReview (K. C. Gupta), ZentralBlatt.

Referenced by:

§28.26(ii).

Encodings:

BibTeX
D. Naylor (1990)
On an asymptotic expansion of the Kontorovich-Lebedev transform,

Applicable Anal. 39 (4), pp. 249–263.

External Links:

ISSN 0003-6811, Document, MathReview (Aloknath Chakrabarti), ZentralBlatt.

Referenced by:

§10.43(v).

Encodings:

BibTeX
D. Naylor (1996)
On an asymptotic expansion of the Kontorovich-Lebedev transform,

Methods Appl. Anal. 3 (1), pp. 98–108.

External Links:

ISSN 1073-2772, FullText, MathReview (C. M. Joshi), ZentralBlatt.

Referenced by:

§10.43(v).

Encodings:

BibTeX
National Bureau of Standards (1958)
Integrals of Airy Functions,

National Bureau of Standards Applied Mathematics Series, U.S. Government Printing Office, Washington, D.C..

External Links:

MathReview (J. C. P. Miller), ZentralBlatt.

Referenced by:

§9.18(v), §9.18(vi).

Encodings:

BibTeX
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..

External Links:

MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §28.1, §28.26(i), §28.35(i).

Encodings:

BibTeX
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.

External Links:

ISSN 0022-2488, Document, MathReview, ZentralBlatt.

Referenced by:

§13.28(i).

Encodings:

BibTeX
M. Neher (2007)
Complex standard functions and their implementation in the CoStLy library,

ACM Trans. Math. Softw. 33 (No. 1, Art. 2), pp. .

Notes:

For the software see CoStLy (free C-XSC library)

External Links:

ISSN 0098-3500, Document.

Referenced by:

§4.48(ii), CoStLy (free C-XSC library).

Encodings:

BibTeX
W. J. Nellis and B. C. Carlson (1966)
Reduction and evaluation of elliptic integrals,

Math. Comp. 20 (94), pp. 223–231.

External Links:

FullText, MathReview (I. A. Stegun), ZentralBlatt.

Referenced by:

¶ ‣ §19.37(iv).

Encodings:

BibTeX
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.

Referenced by:

§2.8(vi).

Encodings:

BibTeX
NetNUMPAC (free Fortran library)

Notes:

Double precision. In Japanese, with some English.

External Links:

Home Page.

Referenced by:

§ ‣ § Software Cross Index.

Encodings:

BibTeX
E. Neuman (1969a)
Elliptic integrals of the second and third kinds,

Zastos. Mat. 11, pp. 99–102.

Notes:

Includes Algol program.

External Links:

MathReview.

Referenced by:

§19.39(iii).

Encodings:

BibTeX
E. Neuman (1969b)
On the calculation of elliptic integrals of the second and third kinds.,

Zastos. Mat. 11, pp. 91–94.

External Links:

MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §19.36(ii).

Encodings:

BibTeX
E. Neuman (2003)
Bounds for symmetric elliptic integrals,

J. Approx. Theory 122 (2), pp. 249–259.

External Links:

ISSN 0021-9045, Document, MathReview (C. M. Joshi), ZentralBlatt.

Referenced by:

¶ ‣ §19.24(ii), §19.24(i), §19.9(i).

Encodings:

BibTeX
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).

External Links:

ISSN 1443-5756, FullText, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §10.14.

Encodings:

BibTeX
P. Nevai (1986)
Géza Freud, orthogonal polynomials and Christoffel functions. A case study,

J. Approx. Theory 48 (1), pp. 3–167.

External Links:

ISSN 0021-9045, Document, MathReview (T. S. Chihara), ZentralBlatt.

Referenced by:

§18.32.

Encodings:

BibTeX
E. H. Neville (1951)
Jacobian Elliptic Functions,

2nd edition, Clarendon Press, Oxford.

External Links:

MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §20.1.

Encodings:

BibTeX
J. N. Newman (1984)
Approximations for the Bessel and Struve functions,

Math. Comp. 43 (168), pp. 551–556.

External Links:

ISSN 0025-5718, FullText, MathReview (S. Conde), ZentralBlatt.

Referenced by:

§11.15(ii).

Encodings:

BibTeX
M. Newman (1967)
Solving equations exactly,

J. Res. Nat. Bur. Standards Sect. B 71B, pp. 171–179.

External Links:

MathReview, ZentralBlatt.

Referenced by:

§27.15.

Encodings:

BibTeX
T. D. Newton (1952)
Coulomb Functions for Large Values of the Parameter $\eta$ ,

Technical report

Atomic Energy of Canada Limited, Chalk River, Ontario.

Notes:

Rep. CRT-526

External Links:

MathReview (A. Erdélyi).

Referenced by:

§33.7.

Encodings:

BibTeX

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.

Notes:

See for additions and corrections same journal, Sect. B 75, 149–163 (1975)

External Links:

MathReview, ZentralBlatt.

Referenced by:

§7.14(iii), §7.21, §7.7(iii).

Encodings:

BibTeX
N. Nielsen (1906a)
Handbuch der Theorie der Gammafunktion,

B. G. Teubner, Leipzig (German).

Notes:

For a reprint with corrections see Nielsen (1965).

External Links:

ZentralBlatt (G. Kowalewski).

Referenced by:

§5.12, Ch.5, §6.10(i), §6.10(i), §7.9, §8.1.

Encodings:

BibTeX
N. Nielsen (1906b)
Theorie des Integrallogarithmus und verwandter Transzendenten,

B. G. Teubner, Leipzig (German).

Notes:

For a reprint with corrections see Nielsen (1965).

External Links:

ZentralBlatt (G. Kowalewski).

Referenced by:

§6.14(i), §6.14(ii), §6.14(iii), §6.7(ii), §6.7(iv), §6.9.

Encodings:

BibTeX
N. Nielsen (1909)
Der Eulersche Dilogarithmus und seine Verallgemeinerungen,

Nova Acta Leopoldina 90, pp. 123–212.

External Links:

ZentralBlatt.

Referenced by:

§25.12(i).

Encodings:

BibTeX
N. Nielsen (1923)
Traité Élémentaire des Nombres de Bernoulli,

Gauthier-Villars, Paris.

External Links:

ZentralBlatt.

Referenced by:

¶ ‣ §24.1.

Encodings:

BibTeX
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).

Notes:

Both books are textually unaltered except for correction of errata.

External Links:

MathReview.

Referenced by:

N. Nielsen (1906a), N. Nielsen (1906b).

Encodings:

BibTeX
Y. Nievergelt (1995)
Bisection hardly ever converges linearly,

Numer. Math. 70 (1), pp. 111–118.

External Links:

ISSN 0029-599X, Document, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §3.8(iii).

Encodings:

BibTeX
A. Nijenhuis and H. S. Wilf (1975)
Combinatorial Algorithms,

Academic Press, New York.

External Links:

ISBN 0-12-519250-9, MathReview (Alon Itai), ZentralBlatt.

Referenced by:

§26.22.

Encodings:

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

Birkhäuser Verlag, Basel.

Notes:

Translated from the Russian and with a preface by Ralph P. Boas, with a foreword by A. A. Samarskiĭ

External Links:

ISBN 3-7643-3183-6, MathReview, ZentralBlatt.

Referenced by:

§18.18(i), §18.39(i), §18.39(i).

Encodings:

BibTeX
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.

External Links:

ISBN 0-471-62546-9, MathReview, ZentralBlatt.

Referenced by:

Ch.27.

Encodings:

BibTeX
NMS (free collection of Fortran subroutines)

Notes:

Single and double precision. See Kahaner et al. (1989).

External Links:

Package NMS (in GAMS).

Referenced by:

§ ‣ § Software Cross Index.

Encodings:

BibTeX
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.

Notes:

Double-precision Fortran code.

External Links:

Document, Code.

Referenced by:

§13.32(ii), §33.26(ii).

Encodings:

BibTeX
C. J. Noble (2004)
Evaluation of negative energy Coulomb (Whittaker) functions,

Comput. Phys. Comm. 159 (1), pp. 55–62.

Notes:

Double-precision Fortran-90 code.

External Links:

Document, Code.

Referenced by:

§33.23(vi), §33.26(ii).

Encodings:

BibTeX
V. A. Noonburg (1995)
A separating surface for the Painlevé differential equation $x^{{\prime\prime}}=x^{2}-t$ ,

J. Math. Anal. Appl. 193 (3), pp. 817–831.

External Links:

ISSN 0022-247X, Document, MathReview (W. S. Loud), ZentralBlatt.

Referenced by:

§32.17.

Encodings:

BibTeX
L. N. Nosova and S. A. Tumarkin (1965)
Tables of Generalized Airy Functions for the Asymptotic Solution of the Differential Equations $\epsilon(py^{{\prime}})^{{\prime}}+(q+\epsilon r)y=f$ ,

Pergamon Press, Oxford.

Notes:

D. E. Brown, translator.

External Links:

MathReview, ZentralBlatt.

Referenced by:

§9.18(vi).

Encodings:

BibTeX
M. Noumi and Y. Yamada (1998)
Affine Weyl groups, discrete dynamical systems and Painlevé equations,

Comm. Math. Phys. 199 (2), pp. 281–295.

External Links:

ISSN 0010-3616, Document, MathReview (Alexander Vladimirovich Kitaev), ZentralBlatt.

Referenced by:

§32.2(v).

Encodings:

BibTeX
M. Noumi and Y. Yamada (1999)
Symmetries in the fourth Painlevé equation and Okamoto polynomials,

Nagoya Math. J. 153, pp. 53–86.

External Links:

ISSN 0027-7630, MathReview (Andrei A. Kapaev), ZentralBlatt.

Referenced by:

§32.8(iv).

Encodings:

BibTeX
M. Noumi (2004)
Painlevé Equations through Symmetry,

Translations of Mathematical Monographs, Vol. 223, American Mathematical Society, Providence, RI.

Notes:

Translated from the 2000 Japanese original by the author

External Links:

ISBN 0-8218-3221-2, MathReview (Andrei A. Kapaev), ZentralBlatt.

Referenced by:

§32.2(v).

Encodings:

BibTeX
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).

Notes:

In Russian. English translation: Sov. Math., Dokl. 30(1988), no. 8, pp. 666–668.

External Links:

ISSN 0002-3264, MathReview (Vojislav Marić), ZentralBlatt.

Referenced by:

§32.11(iv).

Encodings:

BibTeX
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).

Notes:

In Russian. English translation: Math. USSR-Izv. 37(1991), no. 3, pp. 587–609.

External Links:

ISSN 0373-2436, Document, MathReview (Alexander I. Bobenko), ZentralBlatt.

Referenced by:

§32.12(ii).

Encodings:

BibTeX
Number Theory Web (Web Site)

Notes:

References and links to software for factorization and primality testing.

External Links:

Home Page.

Referenced by:

§27.22.

Encodings:

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

Notes:

A large general purpose mathematical software collection containing some special function codes. Implementation is in single precision.

External Links:

Home Page.

Referenced by:

§ ‣ § Software Cross Index.

Encodings:

BibTeX
H. M. Nussenzveig (1965)
High-frequency scattering by an impenetrable sphere,

Ann. Physics 34 (1), pp. 23–95.

External Links:

Document, MathReview (E. Ar).

Referenced by:

§14.31(iii).

Encodings:

BibTeX
J. F. Nye (1999)
Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations,

Institute of Physics Publishing, Bristol.

External Links:

ISBN 0-7503-0610-6, MathReview (Peter Giblin), ZentralBlatt.

Referenced by:

§36.14(ii).

Encodings:

BibTeX
J. F. Nye (2006)
Dislocation lines in the hyperbolic umbilic diffraction catastrophe,

Proc. Roy. Soc. Lond. Ser. A 462, pp. 2299–2313.

External Links:

ISSN 1364-5021, Document, MathReview, ZentralBlatt.

Referenced by:

§36.7(iv).

Encodings:

BibTeX
J. F. Nye (2007)
Dislocation lines in the swallowtail diffraction catastrophe,

Proc. Roy. Soc. Lond. Ser. A 463, pp. 343–355.

External Links:

ISSN 1364-5021, Document, ZentralBlatt.

Referenced by:

§36.7(iv).

Encodings:

BibTeX
G. Németh (1992)
Mathematical Approximation of Special Functions,

Nova Science Publishers Inc., Commack, NY.

Notes:

Ten papers on Chebyshev expansions

External Links:

ISBN 1-56072-052-2, MathReview (N. Hayek Calil), ZentralBlatt.

Referenced by:

¶ ‣ §10.76(ii), ¶ ‣ §10.76(ii), ¶ ‣ §10.76(ii), ¶ ‣ §10.76(iii), §9.19(ii).

Encodings:

BibTeX
N. E. Nörlund (1922)
Mémoire sur les polynomes de Bernoulli,

Acta Math. 43, pp. 121–196 (French).

External Links:

Document.

Referenced by:

§24.13(i), §24.13(ii), §24.14(i), Ch.24.

Encodings:

BibTeX
N. E. Nörlund (1924)
Vorlesungen über Differenzenrechnung,

Springer-Verlag, Berlin (German).

Notes:

Reprinted 1954 by Chelsea Publishing Company, New York

External Links:

ZentralBlatt.

Referenced by:

¶ ‣ §24.1, ¶ ‣ §24.1, §24.13(i), §24.13(ii), ¶ ‣ §24.16(i), ¶ ‣ §24.17(i), §24.17(i), §24.2(i), §24.2(ii), §24.4(i), §24.4(ii), §24.4(iii), §24.4(v), §24.5(i), Ch.24, §25.6(i).

Encodings:

BibTeX
N. E. Nørlund (1955)
Hypergeometric functions,

Acta Math. 94, pp. 289–349.

External Links:

Document, MathReview (A. Erdélyi), ZentralBlatt.

Referenced by:

§16.10, §16.8(ii), §16.8(ii).

Encodings:

BibTeX