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- Notes:
- The NAG Libraries are large general purpose numerical software librarieswith broad coverage of elementary and special functions.Implementations are in single and double precision.
- Referenced by:
- § ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index.
- Encodings:
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- A. Nakamura (1996)Toda equation and its solutions in special functions.J. Phys. Soc. Japan65 (6), pp. 1589–1597.ⓘ
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- §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. Software18 (3), pp. 345–349.ⓘ
- Notes:
- Double-precision Fortran, minimum accuracy 9S,maximum accuracy 13S.
- External Links:
- ISSN 0098-3500,Document,GAMS (module 707; package TOMS),ZentralBlatt
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- 1st item.
- 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.
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- Referenced by:
- §13.32(iii).
- Encodings:
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- A. Natarajan and N. Mohankumar (1993)On the numerical evaluation of the generalised Fermi-Dirac integrals.Comput. Phys. Comm.76 (1), pp. 48–50.ⓘ
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- National Bureau of Standards (1944)Tables of Lagrangian Interpolation Coefficients.Columbia University Press,New York.ⓘ
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- Technical Director: Arnold N. Lowan
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- §3.3(ii).
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- §25.14(ii).
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- §28.26(ii).
- Encodings:
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- 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.ⓘ
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- §28.26(ii).
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- 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.ⓘ
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- 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.ⓘ
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- ISSN 1073-2772,FullText,MathReview (C. M. Joshi),ZentralBlatt
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- §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..ⓘ
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- 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..ⓘ
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- Referenced by:
- §28.1,§28.26(i),6th item,Notations S,Notations S.
- Encodings:
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- 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.ⓘ
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- 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 (1), pp. Article 2.ⓘ
- Notes:
- For the software seeCoStLy (free C-XSC library)
- External Links:
- ISSN 0098-3500,Document
- Referenced by:
- 3rd item,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.ⓘ
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- FullText,MathReview (I. A. Stegun),ZentralBlatt
- Referenced by:
- §19.37(iv).
- Encodings:
- BibTeX
- G. Nemes (2017a)Error bounds for the asymptotic expansion of the Hurwitz zeta function.Proc. A.473 (2203), pp. 20170363, 16.ⓘ
- External Links:
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- Referenced by:
- (25.11.44),(25.11.45),§25.11(xii),§25.11(xii),§8.15,Erratum (V1.2.1) for §25.11(xii),Erratum (V1.2.1) for Addition.
- Encodings:
- BibTeX
- 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.ⓘ
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- Referenced by:
- §8.18(ii),§8.18(ii),Erratum (V1.0.14) for Subsections8.18(ii)–8.11(v).
- Encodings:
- BibTeX
- G. Nemes (2013a)An explicit formula for the coefficients in Laplace’s method.Constr. Approx.38 (3), pp. 471–487.ⓘ
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- Referenced by:
- §5.11(i),§5.11(i).
- Encodings:
- BibTeX
- 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.ⓘ
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- ISSN 1452-8630,Document,FullText,MathReview (Junesang Choi),ZentralBlatt
- Referenced by:
- §5.11(ii),§5.11(ii).
- Encodings:
- BibTeX
- G. Nemes (2013c)Generalization of Binet’s Gamma function formulas.Integral Transforms Spec. Funct.24 (8), pp. 597–606.ⓘ
- External Links:
- ISSN 1065-2469,Document,FullText,MathReview (Daniele Ritelli),ZentralBlatt
- Referenced by:
- §5.11(i),§5.11(i).
- Encodings:
- BibTeX
- 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.ⓘ
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- ISSN 1364-5021,MathReview (Mehdi Hassani),ZentralBlatt
- Referenced by:
- §5.17,§5.17.
- Encodings:
- BibTeX
- 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.ⓘ
- External Links:
- ISSN 1848-5979,Document,Link,MathReview (José Luis López),ZentralBlatt
- Referenced by:
- (11.11.10),(11.11.8),§11.11(iii).
- Encodings:
- BibTeX
- 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.ⓘ
- External Links:
- ISSN 1848-5979,Document,Link,MathReview Entry,ZentralBlatt
- Referenced by:
- (11.11.10),(11.11.8),§11.11(iii).
- Encodings:
- BibTeX
- 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.ⓘ
- External Links:
- ISSN 0308-2105,Document,Link,MathReview Entry,ZentralBlatt
- Referenced by:
- §5.11(i),§5.11(i).
- Encodings:
- BibTeX
- G. Nemes (2015b)On the large argument asymptotics of the Lommel function via Stieltjes transforms.Asymptot. Anal.91 (3-4), pp. 265–281.ⓘ
- External Links:
- ISSN 0921-7134,Document,MathReview Entry,ZentralBlatt
- Referenced by:
- §11.6(iii),§11.6(iii),§11.9(iii),§11.9(iii).
- Encodings:
- BibTeX
- G. Nemes (2015c)The resurgence properties of the incomplete gamma function II.Stud. Appl. Math.135 (1), pp. 86–116.ⓘ
- External Links:
- ISSN 0022-2526,Document,Link,MathReview Entry,ZentralBlatt
- Referenced by:
- §8.11(iii).
- Encodings:
- BibTeX
- G. Nemes (2016)The resurgence properties of the incomplete gamma function, I.Anal. Appl. (Singap.)14 (5), pp. 631–677.ⓘ
- External Links:
- ISSN 0219-5305,Document,Link,MathReview Entry,ZentralBlatt
- Referenced by:
- §8.11(iii),§8.11(v),§8.11(v),Erratum (V1.0.14) for Subsections8.18(ii)–8.11(v).
- Encodings:
- BibTeX
- G. Nemes (2017b)Error Bounds for the Large-Argument Asymptotic Expansions of the Hankel and Bessel Functions.Acta Appl. Math.150, pp. 141–177.ⓘ
- External Links:
- ISSN 0167-8019,Document,MathReview Entry,ZentralBlatt
- Referenced by:
- (9.7.16),(9.7.17),§9.7(iii),§9.7(iv).
- Encodings:
- BibTeX
- 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.ⓘ
- External Links:
- ISSN 0022-2526,Document,Link,MathReview (Pedro J. Pagola),ZentralBlatt
- Referenced by:
- §11.11(i),§11.11(i).
- Encodings:
- BibTeX
- G. Nemes (2020)An extension of Laplace’s method.Constr. Approx.51 (2), pp. 247–272.ⓘ
- External Links:
- ISSN 0176-4276,Document,Link,MathReview (José Luis López),ZentralBlatt
- Referenced by:
- (11.11.16),(11.11.17),§11.11(iii).
- Encodings:
- BibTeX
- 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.ⓘ
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- ISSN 0036-1410,Document,Link,MathReview (José Luis López),ZentralBlatt
- Referenced by:
- (10.18.17),(10.18.18),§10.18(iii),(9.8.22),(9.8.23),§9.8(iv),Erratum (V1.1.8) for Section9.8(iv),Erratum (V1.1.8) for Section10.18(iii).
- 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),2nd item.
- 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.
- NetNUMPAC (free Fortran library)ⓘ
- Notes:
- Double precision. In Japanese, with some English.
- External Links:
- Home Page
- Referenced by:
- § ‣Software Cross Index.
- Encodings:
- BibTeX
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- 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. Theory122 (2), pp. 249–259.ⓘ
- External Links:
- ISSN 0021-9045,Document,MathReview (C. M. Joshi),ZentralBlatt
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- §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).ⓘ
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- Referenced by:
- §10.14.
- Encodings:
- BibTeX
- E. Neuman (2013)Inequalities and bounds for the incomplete gamma function.Results Math.63 (3-4), pp. 1209–1214.ⓘ
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- §8.10,§8.10.
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- §18.32.
- Encodings:
- BibTeX
- E. H. Neville (1951)Jacobian Elliptic Functions.2nd edition,Clarendon Press,Oxford.ⓘ
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- Encodings:
- BibTeX
- J. N. Newman (1984)Approximations for the Bessel and Struve functions.Math. Comp.43 (168), pp. 551–556.ⓘ
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- 1st item.
- Encodings:
- BibTeX
- M. Newman (1967)Solving equations exactly.J. Res. Nat. Bur. Standards Sect. B71B, pp. 171–179.ⓘ
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- BibTeX
- R. G. Newton (2002)Scattering theory of waves and particles.Dover Publications, Inc., Mineola, NY.ⓘ
- Notes:
- Reprint of the 1982 second edition [Springer, New York;MR0666397 (84f:81001)], with list of errata prepared for thisedition by the author
- External Links:
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- §1.18(vi),§1.18(viii).
- Encodings:
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- T. D. Newton (1952)Coulomb Functions for Large Values of the Parameter. Technical reportAtomic Energy of Canada Limited, ChalkRiver, Ontario.ⓘ
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- Rep. CRT-526
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- §33.7.
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- §7.14(iii),§7.21,§7.7(iii).
- Encodings:
- BibTeX
- 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).ⓘ
- Notes:
- For a reprint with corrections seeNielsen (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 Leopoldina90, pp. 123–212.ⓘ
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- Referenced by:
- §25.12(i).
- Encodings:
- BibTeX
- N. Nielsen (1923)Traité Élémentaire des Nombres de Bernoulli.Gauthier-Villars,Paris.ⓘ
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- 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
- 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.ⓘ
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- Referenced by:
- (18.39.17),(18.39.18).
- 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
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- §3.8(iii).
- Encodings:
- BibTeX
- A. Nijenhuis and H. S. Wilf (1975)Combinatorial Algorithms.Academic Press,New York.ⓘ
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- ISBN 0-12-519250-9,MathReview (Alon Itai),ZentralBlatt
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- §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),Erratum (V1.2.0) §18.39.
- Encodings:
- BibTeX
- G. Nikolov and V. Pillwein (2015)An extension of Turán’s inequality.Math. Inequal. Appl.18 (1), pp. 321–335.ⓘ
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- ISSN 1331-4343,Document,Link,MathReview (Gradimir V. Milovanovic),ZentralBlatt
- Referenced by:
- §18.14(ii).
- 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. SeeKahaner et al. (1989).
- External Links:
- GAMS (package NMS)
- Referenced by:
- § ‣Software Cross Index,§ ‣Software Cross Index,§ ‣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.
- 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),8th item.
- Encodings:
- BibTeX
- V. A. Noonburg (1995)A separating surface for the Painlevé differential equation.J. Math. Anal. Appl.193 (3), pp. 817–831.ⓘ
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- ISSN 0022-247X,Document,MathReview (W. S. Loud),ZentralBlatt
- Referenced by:
- §32.17.
- Encodings:
- BibTeX
- N. E. Nørlund (1955)Hypergeometric functions.Acta Math.94, pp. 289–349.ⓘ
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- Document,MathReview (A. Erdélyi),ZentralBlatt
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- Encodings:
- BibTeX
- N. E. Nörlund (1922)Mémoire sur les polynomes de Bernoulli.Acta Math.43, pp. 121–196 (French).ⓘ
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- §24.13(i),§24.13(ii),§24.14(i),Ch.24.
- Encodings:
- BibTeX
- N. E. Nörlund (1924)Vorlesungen über Differenzenrechnung.Springer-Verlag,Berlin (German).
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- D. E. Brown, translator.
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- 4th item.
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- BibTeX
- M. Noumi and J. V. Stokman (2004)Askey-Wilson polynomials: an affine Hecke algebra approach.InLaredo Lectures on Orthogonal Polynomials and SpecialFunctions,Adv. Theory Spec. Funct. Orthogonal Polynomials, pp. 111–144.ⓘ
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- §18.38(iii).
- 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.ⓘ
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- 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.ⓘ
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- 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 SSSR283 (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 (website)
- Numerical Recipes (commercial C, C++, Fortran 77, and Fortran 90 libraries)ⓘ
- Notes:
- A large general purpose mathematical software collection containing somespecial function codes. Implementation is in single precision.
- External Links:
- Home Page
- Referenced by:
- § ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index,§ ‣Software Cross Index.
- Encodings:
- BibTeX
- H. M. Nussenzveig (1965)High-frequency scattering by an impenetrable sphere.Ann. Physics34 (1), pp. 23–95.ⓘ
- External Links:
- Document,MathReview (E. Ar)
- Referenced by:
- §14.31(iii).
- Encodings:
- BibTeX
- 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.ⓘ
- 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. A462, 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. A463, pp. 343–355.ⓘ
- External Links:
- ISSN 1364-5021,Document,ZentralBlatt
- Referenced by:
- §36.7(iv).
- Encodings:
- BibTeX
