Bibliography L
-
G. Labahn and M. Mutrie (1997)
Reduction of Elliptic Integrals to Legendre Normal Form.
Technical report
Technical Report 97-21, Department of Computer Science, University of Waterloo, Waterloo, Ontario.
-
A. Laforgia and M. E. Muldoon (1983)
Inequalities and approximations for zeros of Bessel functions of small order.
SIAM J. Math. Anal. 14 (2), pp. 383–388.
-
A. Laforgia and M. E. Muldoon (1988)
Monotonicity properties of zeros of generalized Airy functions.
Z. Angew. Math. Phys. 39 (2), pp. 267–271.
-
A. Laforgia and S. Sismondi (1988)
Monotonicity results and inequalities for the gamma and error functions.
J. Comput. Appl. Math. 23 (1), pp. 25–33.
-
A. Laforgia (1979)
On the Zeros of the Derivative of Bessel Functions of Second Kind.
Pubblicazioni Serie III [Publication Series III], Vol. 179, Istituto per le Applicazioni del Calcolo “Mauro Picone” (IAC), Rome.
-
A. Laforgia (1984)
Further inequalities for the gamma function.
Math. Comp. 42 (166), pp. 597–600.
-
A. Laforgia (1986)
Inequalities for Bessel functions.
J. Comput. Appl. Math. 15 (1), pp. 75–81.
-
A. Laforgia (1991)
Bounds for modified Bessel functions.
J. Comput. Appl. Math. 34 (3), pp. 263–267.
-
J. C. Lagarias, V. S. Miller, and A. M. Odlyzko (1985)
Computing : The Meissel-Lehmer method.
Math. Comp. 44 (170), pp. 537–560.
-
J. Lagrange (1770)
Démonstration d’un Théoréme d’Arithmétique.
Nouveau Mém. Acad. Roy. Sci. Berlin, pp. 123–133 (French).
-
S. Lai and Y. Chiu (1990)
Exact computation of the - and - symbols.
Comput. Phys. Comm. 61 (3), pp. 350–360.
-
S. Lai and Y. Chiu (1992)
Exact computation of the - symbols.
Comput. Phys. Comm. 70 (3), pp. 544–556.
-
V. Laĭ (1994)
The two-point connection problem for differential equations of the Heun class.
Teoret. Mat. Fiz. 101 (3), pp. 360–368 (Russian).
-
H. Lamb (1932)
Hydrodynamics.
6th edition, Cambridge University Press, Cambridge.
-
C. G. Lambe and D. R. Ward (1934)
Some differential equations and associated integral equations.
Quart. J. Math. (Oxford) 5, pp. 81–97.
-
C. G. Lambe (1952)
Lamé-Wangerin functions.
Quart. J. Math., Oxford Ser. (2) 3, pp. 107–114.
-
E. Landau (1953)
Handbuch der Lehre von der Verteilung der Primzahlen. 2 Bände.
Chelsea Publishing Co., New York (German).
-
L. D. Landau and E. M. Lifshitz (1962)
The Classical Theory of Fields.
Pergamon Press, Oxford.
-
L. D. Landau and E. M. Lifshitz (1965)
Quantum Mechanics: Non-relativistic Theory.
Pergamon Press Ltd., Oxford.
-
L. D. Landau and E. M. Lifshitz (1987)
Fluid Mechanics.
2nd edition, Pergamon Press, London.
-
L. J. Landau (1999)
Ratios of Bessel functions and roots of .
J. Math. Anal. Appl. 240 (1), pp. 174–204.
-
L. J. Landau (2000)
Bessel functions: Monotonicity and bounds.
J. London Math. Soc. (2) 61 (1), pp. 197–215.
-
S. Lang (1987)
Elliptic Functions.
2nd edition, Graduate Texts in Mathematics, Vol. 112, Springer-Verlag, New York.
-
R. E. Langer (1934)
The solutions of the Mathieu equation with a complex variable and at least one parameter large.
Trans. Amer. Math. Soc. 36 (3), pp. 637–695.
-
L. Lapointe and L. Vinet (1996)
Exact operator solution of the Calogero-Sutherland model.
Comm. Math. Phys. 178 (2), pp. 425–452.
-
T. M. Larsen, D. Erricolo, and P. L. E. Uslenghi (2009)
New method to obtain small parameter power series expansions of Mathieu radial and angular functions.
Math. Comp. 78 (265), pp. 255–274.
-
H. T. Lau (1995)
A Numerical Library in C for Scientists and Engineers.
CRC Press, Boca Raton, FL.
-
H. T. Lau (2004)
A Numerical Library in Java for Scientists & Engineers.
Chapman & Hall/CRC, Boca Raton, FL.
-
B. J. Laurenzi (1993)
Moment integrals of powers of Airy functions.
Z. Angew. Math. Phys. 44 (5), pp. 891–908.
-
H. A. Lauwerier (1974)
Asymptotic Analysis.
Mathematical Centre Tracts, Mathematisch Centrum, Amsterdam.
-
D. F. Lawden (1989)
Elliptic Functions and Applications.
Applied Mathematical Sciences, Vol. 80, Springer-Verlag, New York.
-
P. W. Lawrence, R. M. Corless, and D. J. Jeffrey (2012)
Algorithm 917: complex double-precision evaluation of the Wright function.
ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.
-
W. Lay, K. Bay, and S. Yu. Slavyanov (1998)
Asymptotic and numeric study of eigenvalues of the double confluent Heun equation.
J. Phys. A 31 (42), pp. 8521–8531.
-
W. Lay and S. Yu. Slavyanov (1998)
The central two-point connection problem for the Heun class of ODEs.
J. Phys. A 31 (18), pp. 4249–4261.
-
W. Lay and S. Yu. Slavyanov (1999)
Heun’s equation with nearby singularities.
Proc. Roy. Soc. London Ser. A 455, pp. 4347–4361.
-
D. Le (1985)
An efficient derivative-free method for solving nonlinear equations.
ACM Trans. Math. Software 11 (3), pp. 250–262.
-
E. W. Leaver (1986)
Solutions to a generalized spheroidal wave equation: Teukolsky’s equations in general relativity, and the two-center problem in molecular quantum mechanics.
J. Math. Phys. 27 (5), pp. 1238–1265.
-
A. V. Lebedev and R. M. Fedorova (1960)
A Guide to Mathematical Tables.
Pergamon Press, Amsterdam-New York-Oxford.
-
N. N. Lebedev, I. P. Skalskaya, and Y. S. Uflyand (1965)
Problems of Mathematical Physics.
Revised, enlarged and corrected English edition; translated
and edited by Richard A. Silverman. With a supplement by
Edward L. Reiss, Prentice-Hall Inc., Englewood Cliffs, N.J..
-
N. N. Lebedev (1965)
Special Functions and Their Applications.
Prentice-Hall Inc., Englewood Cliffs, N.J..
-
J. LeCaine (1945)
A table of integrals involving the functions .
-
D. K. Lee (1990)
Application of theta functions for numerical evaluation of complete elliptic integrals of the first and second kinds.
Comput. Phys. Comm. 60 (3), pp. 319–327.
-
Soo-Y. Lee (1980)
The inhomogeneous Airy functions, and .
J. Chem. Phys. 72 (1), pp. 332–336.
-
W. R. Leeb (1979)
Algorithm 537: Characteristic values of Mathieu’s differential equation.
ACM Trans. Math. Software 5 (1), pp. 112–117.
-
D. J. Leeming (1977)
An asymptotic estimate for the Bernoulli and Euler numbers.
Canad. Math. Bull. 20 (1), pp. 109–111.
-
D. J. Leeming (1989)
The real zeros of the Bernoulli polynomials.
J. Approx. Theory 58 (2), pp. 124–150.
-
A. M. Legendre (1808)
Essai sur la Théorie des Nombres.
2nd edition, Courcier, Paris.
-
A. M. Legendre (1825)
Traité des fonctions elliptiques et des intégrales Eulériennes.
Huzard-Courcier, Paris.
-
D. R. Lehman and J. S. O’Connell (1973)
Graphical Recoupling of Angular Momenta.
Technical report
U.S. Government Printing Office, National Bureau of Standards, Washington, D.C..
-
D. R. Lehman, W. C. Parke, and L. C. Maximon (1981)
Numerical evaluation of integrals containing a spherical Bessel function by product integration.
J. Math. Phys. 22 (7), pp. 1399–1413.
-
D. H. Lehmer (1943)
Ramanujan’s function .
Duke Math. J. 10 (3), pp. 483–492.
-
D. H. Lehmer (1947)
The vanishing of Ramanujan’s function .
Duke Math. J. 14 (2), pp. 429–433.
-
D. H. Lehmer (1940)
On the maxima and minima of Bernoulli polynomials.
Amer. Math. Monthly 47 (8), pp. 533–538.
-
D. H. Lehmer (1941)
Guide to Tables in the Theory of Numbers.
Bulletin of the National Research Council, No. 105, National Research Council, Washington, D.C..
-
D. N. Lehmer (1914)
List of Prime Numbers from 1 to 10,006,721.
Publ. No. 165, Carnegie Institution of Washington, Washington, D.C..
-
J. Lehner (1941)
A partition function connected with the modulus five.
Duke Math. J. 8 (4), pp. 631–655.
-
O. Lehto and K. I. Virtanen (1973)
Quasiconformal Mappings in the Plane.
2nd edition, Springer-Verlag, New York.
-
A. Leitner and J. Meixner (1960)
Eine Verallgemeinerung der Sphäroidfunktionen.
Arch. Math. 11, pp. 29–39.
-
D. Lemoine (1997)
Optimal cylindrical and spherical Bessel transforms satisfying bound state boundary conditions.
Comput. Phys. Comm. 99 (2-3), pp. 297–306.
-
W. J. Lentz (1976)
Generating Bessel functions in Mie scattering calculations using continued fractions.
Applied Optics 15 (3), pp. 668–671.
-
D. A. Leonard (1982)
Orthogonal polynomials, duality and association schemes.
SIAM J. Math. Anal. 13 (4), pp. 656–663.
-
N. L. Lepe (1985)
Functions on a parabolic cylinder with a negative integer index.
Differ. Uravn. 21 (11), pp. 2001–2003, 2024 (Russian).
-
J. Lepowsky and S. Milne (1978)
Lie algebraic approaches to classical partition identities.
Adv. in Math. 29 (1), pp. 15–59.
-
J. Lepowsky and R. L. Wilson (1982)
A Lie theoretic interpretation and proof of the Rogers-Ramanujan identities.
Adv. in Math. 45 (1), pp. 21–72.
-
M. Lerch (1887)
Note sur la fonction .
Acta Math. 11 (1-4), pp. 19–24 (French).
-
M. Lerch (1903)
Zur Theorie der Gaußschen Summen.
Math. Ann. 57 (4), pp. 554–567 (German).
-
M. Lerch (1905)
Einiges über den Integrallogarithmus.
Monatsh. Math. Phys. 16 (1), pp. 125–134.
-
J. Letessier, G. Valent, and J. Wimp (1994)
Some Differential Equations Satisfied by Hypergeometric Functions.
In Approximation and Computation (West Lafayette, IN, 1993),
Internat. Ser. Numer. Math., Vol. 119, pp. 371–381.
-
J. Letessier (1995)
Co-recursive associated Jacobi polynomials.
J. Comput. Appl. Math. 57 (1-2), pp. 203–213.
-
C. Leubner and H. Ritsch (1986)
A note on the uniform asymptotic expansion of integrals with coalescing endpoint and saddle points.
J. Phys. A 19 (3), pp. 329–335.
-
K. V. Leung and S. S. Ghaderpanah (1979)
An application of the finite element approximation method to find the complex zeros of the modified Bessel function .
Math. Comp. 33 (148), pp. 1299–1306.
-
L. Levey and L. B. Felsen (1969)
On incomplete Airy functions and their application to diffraction problems.
Radio Sci. 4 (10), pp. 959–969.
-
E. Levin and D. S. Lubinsky (2001)
Orthogonal Polynomials for Exponential Weights.
CMS Books in Mathematics/Ouvrages de Mathématiques de la
SMC, 4, Springer-Verlag, New York.
-
D. A. Levine (1969)
Algorithm 344: Student’s t-distribution [S14].
Comm. ACM 12 (1), pp. 37–38.
-
H. Levine and J. Schwinger (1948)
On the theory of diffraction by an aperture in an infinite plane screen. I.
Phys. Rev. 74 (8), pp. 958–974.
-
N. Levinson and R. M. Redheffer (1970)
Complex Variables.
Holden-Day Inc., San Francisco, CA.
-
N. Levinson (1974)
More than one third of zeros of Riemann’s zeta-function are on .
Advances in Math. 13 (4), pp. 383–436.
-
J. S. Lew (1994)
On the Darling-Mandelbrot probability density and the zeros of some incomplete gamma functions.
Constr. Approx. 10 (1), pp. 15–30.
-
S. Lewanowicz (1985)
Recurrence relations for hypergeometric functions of unit argument.
Math. Comp. 45 (172), pp. 521–535.
-
S. Lewanowicz (1987)
Corrigenda: “Recurrence relations for hypergeometric functions of unit argument” [Math. Comp. 45 (1985), no. 172, 521–535; MR 86m:33004].
Math. Comp. 48 (178), pp. 853.
-
S. Lewanowicz (1991)
Evaluation of Bessel function integrals with algebraic singularities.
J. Comput. Appl. Math. 37 (1-3), pp. 101–112.
-
L. Lewin (1981)
Polylogarithms and Associated Functions.
North-Holland Publishing Co., New York.
-
J. T. Lewis and M. E. Muldoon (1977)
Monotonicity and convexity properties of zeros of Bessel functions.
SIAM J. Math. Anal. 8 (1), pp. 171–178.
-
L.-W. Li, M. Leong, T.-S. Yeo, P.-S. Kooi, and K.-Y. Tan (1998a)
Computations of spheroidal harmonics with complex arguments: A review with an algorithm.
Phys. Rev. E 58 (5), pp. 6792–6806.
-
L.-W. Li, T. S. Yeo, P. S. Kooi, and M. S. Leong (1998b)
Microwave specific attenuation by oblate spheroidal raindrops: An exact analysis of TCS’s in terms of spheroidal wave functions.
J. Electromagn. Waves Appl. 12 (6), pp. 709–711.
-
X. Li and R. Wong (1994)
Error bounds for asymptotic expansions of Laplace convolutions.
SIAM J. Math. Anal. 25 (6), pp. 1537–1553.
-
X. Li and R. Wong (2000)
A uniform asymptotic expansion for Krawtchouk polynomials.
J. Approx. Theory 106 (1), pp. 155–184.
-
X. Li and R. Wong (2001)
On the asymptotics of the Meixner-Pollaczek polynomials and their zeros.
Constr. Approx. 17 (1), pp. 59–90.
-
X. Li, X. Shi, and J. Zhang (1991)
Generalized Riemann -function regularization and Casimir energy for a piecewise uniform string.
Phys. Rev. D 44 (2), pp. 560–562.
-
Y. T. Li and R. Wong (2008)
Integral and series representations of the Dirac delta function.
Commun. Pure Appl. Anal. 7 (2), pp. 229–247.
-
Y. A. Li and P. J. Olver (2000)
Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation.
J. Differential Equations 162 (1), pp. 27–63.
-
E. M. Lifshitz and L. P. Pitaevskiĭ (1980)
Statistical Physics, Part 2: Theory of the Condensed State.
Pergamon Press, Oxford.
-
M. J. Lighthill (1958)
An Introduction to Fourier Analysis and Generalised Functions.
Cambridge Monographs on Mechanics and Applied Mathematics, Cambridge University Press, New York.
-
Y. Lin and R. Wong (2013)
Global asymptotics of the Hahn polynomials.
Anal. Appl. (Singap.) 11 (3), pp. 1350018, 47.
-
E. Lindelöf (1905)
Le Calcul des Résidus et ses Applications à la Théorie des Fonctions.
Gauthier-Villars, Paris (French).
-
P. Linz and T. E. Kropp (1973)
A note on the computation of integrals involving products of trigonometric and Bessel functions.
Math. Comp. 27 (124), pp. 871–872.
-
J. E. Littlewood (1914)
Sur la distribution des nombres premiers.
Comptes Rendus de l’Academie des Sciences, Paris 158, pp. 1869–1872 (French).
-
M. Yu. Loenko (2001)
Evaluating elementary functions with guaranteed precision.
Programming and Computer Software 27 (2), pp. 101–110.
-
I. M. Longman (1956)
Note on a method for computing infinite integrals of oscillatory functions.
Proc. Cambridge Philos. Soc. 52 (4), pp. 764–768.
-
J. L. López (2001)
Uniform asymptotic expansions of symmetric elliptic integrals.
Constr. Approx. 17 (4), pp. 535–559.
-
J. L. López and P. J. Pagola (2010)
The confluent hypergeometric functions and for large and .
J. Comput. Appl. Math. 233 (6), pp. 1570–1576.
-
J. L. López and P. J. Pagola (2011)
A systematic “saddle point near a pole” asymptotic method with application to the Gauss hypergeometric function.
Stud. Appl. Math. 127 (1), pp. 24–37.
-
J. L. López, P. Pagola, and E. Pérez Sinusía (2013a)
Asymptotics of the first Appell function with large parameters II.
Integral Transforms Spec. Funct. 24 (12), pp. 982–999.
-
J. L. López, P. Pagola, and E. Pérez Sinusía (2013b)
Asymptotics of the first Appell function with large parameters.
Integral Transforms Spec. Funct. 24 (9), pp. 715–733.
-
J. L. López and E. Pérez Sinusía (2014)
New series expansions for the confluent hypergeometric function .
Appl. Math. Comput. 235, pp. 26–31.
-
J. L. López and N. M. Temme (1999a)
Approximation of orthogonal polynomials in terms of Hermite polynomials.
Methods Appl. Anal. 6 (2), pp. 131–146.
-
J. L. López and N. M. Temme (1999b)
Hermite polynomials in asymptotic representations of generalized Bernoulli, Euler, Bessel, and Buchholz polynomials.
J. Math. Anal. Appl. 239 (2), pp. 457–477.
-
J. L. López and N. M. Temme (1999c)
Uniform approximations of Bernoulli and Euler polynomials in terms of hyperbolic functions.
Stud. Appl. Math. 103 (3), pp. 241–258.
-
J. L. López and N. M. Temme (2013)
New series expansions of the Gauss hypergeometric function.
Adv. Comput. Math. 39 (2), pp. 349–365.
-
J. L. López (1999)
Asymptotic expansions of the Whittaker functions for large order parameter.
Methods Appl. Anal. 6 (2), pp. 249–256.
-
J. L. López (2000)
Asymptotic expansions of symmetric standard elliptic integrals.
SIAM J. Math. Anal. 31 (4), pp. 754–775.
-
J. L. López and N. M. Temme (2010a)
Asymptotics and numerics of polynomials used in Tricomi and Buchholz expansions of Kummer functions.
Numer. Math. 116 (2), pp. 269–289.
-
J. L. López and N. M. Temme (2010b)
Large degree asymptotics of generalized Bernoulli and Euler polynomials.
J. Math. Anal. Appl. 363 (1), pp. 197–208.
-
L. Lorch (1992)
On Bessel functions of equal order and argument.
Rend. Sem. Mat. Univ. Politec. Torino 50 (2), pp. 209–216 (1993).
-
L. Lorch, M. E. Muldoon, and P. Szegő (1970)
Higher monotonicity properties of certain Sturm-Liouville functions. III.
Canad. J. Math. 22, pp. 1238–1265.
-
L. Lorch, M. E. Muldoon, and P. Szegő (1972)
Higher monotonicity properties of certain Sturm-Liouville functions. IV.
Canad. J. Math. 24, pp. 349–368.
-
L. Lorch and M. E. Muldoon (2008)
Monotonic sequences related to zeros of Bessel functions.
Numer. Algorithms 49 (1-4), pp. 221–233.
-
L. Lorch and P. Szegő (1963)
Higher monotonicity properties of certain Sturm-Liouville functions..
Acta Math. 109, pp. 55–73.
-
L. Lorch and P. Szegő (1964)
Monotonicity of the differences of zeros of Bessel functions as a function of order.
Proc. Amer. Math. Soc. 15 (1), pp. 91–96.
-
L. Lorch and P. Szegő (1990)
On the points of inflection of Bessel functions of positive order. I.
Canad. J. Math. 42 (5), pp. 933–948.
-
L. Lorch and P. Szegő (1995)
Monotonicity of the zeros of the third derivative of Bessel functions.
Methods Appl. Anal. 2 (1), pp. 103–111.
-
L. Lorch (1984)
Inequalities for ultraspherical polynomials and the gamma function.
J. Approx. Theory 40 (2), pp. 115–120.
-
L. Lorch (1990)
Monotonicity in terms of order of the zeros of the derivatives of Bessel functions.
Proc. Amer. Math. Soc. 108 (2), pp. 387–389.
-
L. Lorch (1993)
Some inequalities for the first positive zeros of Bessel functions.
SIAM J. Math. Anal. 24 (3), pp. 814–823.
-
L. Lorch (1995)
The zeros of the third derivative of Bessel functions of order less than one.
Methods Appl. Anal. 2 (2), pp. 147–159.
-
L. Lorch (2002)
Comparison of a pair of upper bounds for a ratio of gamma functions.
Math. Balkanica (N.S.) 16 (1-4), pp. 195–202.
-
Lord Kelvin (1891)
Popular Lectures and Addresses.
Vol. 3, pp. 481–488.
-
Lord Kelvin (1905)
Deep water ship-waves.
Phil. Mag. 9, pp. 733–757.
-
Lord Rayleigh (1945)
The Theory of Sound.
2nd edition, Dover Publications, New York.
-
H. A. Lorentz, A. Einstein, H. Minkowski, and H. Weyl (1923)
The Principle of Relativity: A Collection of Original Memoirs on the Special and General Theory of Relativity.
Methuen and Co., Ltd., London.
-
L. Lorentzen and H. Waadeland (1992)
Continued Fractions with Applications.
Studies in Computational Mathematics, North-Holland Publishing Co., Amsterdam.
-
H. Lotsch and M. Gray (1964)
Algorithm 244: Fresnel integrals.
Comm. ACM 7 (11), pp. 660–661.
-
J. D. Louck (1958)
New recursion relation for the Clebsch-Gordan coefficients.
Phys. Rev. (2) 110 (4), pp. 815–816.
-
L. Lovász, L. Pyber, D. J. A. Welsh, and G. M. Ziegler (1995)
Combinatorics in Pure Mathematics.
In Handbook of Combinatorics, Vol. 2, R. L. Graham, M. Grötschel, and L. Lovász (Eds.),
pp. 2039–2082.
-
E. R. Love (1970)
Changing the order of integration.
J. Austral. Math. Soc. 11, pp. 421–432.
-
E. R. Love (1972a)
Addendum to: “Changing the order of integration”.
J. Austral. Math. Soc. 14, pp. 383–384.
-
E. R. Love (1972b)
Two index laws for fractional integrals and derivatives.
J. Austral. Math. Soc. 14, pp. 385–410.
-
A. N. Lowan and W. Horenstein (1942)
On the function .
J. Math. Phys. Mass. Inst. Tech. 21, pp. 264–283.
-
T. A. Lowdon (1970)
Integral representation of the Hankel function in terms of parabolic cylinder functions.
Quart. J. Mech. Appl. Math. 23 (3), pp. 315–327.
-
D. W. Lozier and F. W. J. Olver (1993)
Airy and Bessel Functions by Parallel Integration of ODEs.
In Proceedings of the Sixth SIAM Conference on Parallel
Processing for Scientific Computing, R. F. Sincovec, D. E. Keyes, M. R. Leuze, L. R. Petzold, and D. A. Reed (Eds.),
Philadelphia, PA, pp. 530–538.
-
D. W. Lozier and F. W. J. Olver (1994)
Numerical Evaluation of Special Functions.
In Mathematics of Computation 1943–1993: A Half-Century of
Computational Mathematics (Vancouver, BC, 1993),
Proc. Sympos. Appl. Math., Vol. 48, pp. 79–125.
-
D. W. Lozier and J. M. Smith (1981)
Algorithm 567: Extended-range arithmetic and normalized Legendre polynomials [A1], [C1].
ACM Trans. Math. Software 7 (1), pp. 141–146.
-
D. W. Lozier (1980)
Numerical Solution of Linear Difference Equations.
NBSIR
Technical Report 80-1976, National Bureau of Standards, Gaithersburg, MD 20899.
-
D. W. Lozier (1993)
An underflow-induced graphics failure solved by SLI arithmetic.
In IEEE Symposium on Computer Arithmetic, E. E. Swartzlander, M. J. Irwin, and G. A. Jullien (Eds.),
Washington, D.C., pp. 10–17.
-
É. Lucas (1891)
Théorie des nombres. Tome I: Le calcul des nombres entiers, le calcul des nombres rationnels, la divisibilité arithmétique.
Gauthier-Villars, Paris (French).
-
S. K. Lucas and H. A. Stone (1995)
Evaluating infinite integrals involving Bessel functions of arbitrary order.
J. Comput. Appl. Math. 64 (3), pp. 217–231.
-
S. K. Lucas (1995)
Evaluating infinite integrals involving products of Bessel functions of arbitrary order.
J. Comput. Appl. Math. 64 (3), pp. 269–282.
-
D. Ludwig (1966)
Uniform asymptotic expansions at a caustic.
Comm. Pure Appl. Math. 19, pp. 215–250.
-
N. A. Lukaševič and A. I. Yablonskiĭ (1967)
On a set of solutions of the sixth Painlevé equation.
Differ. Uravn. 3 (3), pp. 520–523 (Russian).
-
N. A. Lukaševič (1965)
Elementary solutions of certain Painlevé equations.
Differ. Uravn. 1 (3), pp. 731–735 (Russian).
-
N. A. Lukaševič (1967a)
Theory of the fourth Painlevé equation.
Differ. Uravn. 3 (5), pp. 771–780 (Russian).
-
N. A. Lukaševič (1967b)
On the theory of Painlevé’s third equation.
Differ. Uravn. 3 (11), pp. 1913–1923 (Russian).
-
N. A. Lukaševič (1968)
Solutions of the fifth Painlevé equation.
Differ. Uravn. 4 (8), pp. 1413–1420 (Russian).
-
N. A. Lukaševič (1971)
The second Painlevé equation.
Differ. Uravn. 7 (6), pp. 1124–1125 (Russian).
-
Y. L. Luke and J. Wimp (1963)
Jacobi polynomial expansions of a generalized hypergeometric function over a semi-infinite ray.
Math. Comp. 17 (84), pp. 395–404.
-
Y. L. Luke (1959)
Expansion of the confluent hypergeometric function in series of Bessel functions.
Math. Tables Aids Comput. 13 (68), pp. 261–271.
-
Y. L. Luke (1962)
Integrals of Bessel Functions.
McGraw-Hill Book Co., Inc., New York.
-
Y. L. Luke (1968)
Approximations for elliptic integrals.
Math. Comp. 22 (103), pp. 627–634.
-
Y. L. Luke (1969a)
The Special Functions and their Approximations, Vol. 1.
Academic Press, New York.
-
Y. L. Luke (1969b)
The Special Functions and their Approximations. Vol. 2.
Academic Press, New York.
-
Y. L. Luke (1970)
Further approximations for elliptic integrals.
Math. Comp. 24 (109), pp. 191–198.
-
Y. L. Luke (1971a)
Miniaturized tables of Bessel functions. II.
Math. Comp. 25 (116), pp. 789–795 and D14–E13.
-
Y. L. Luke (1971b)
Miniaturized tables of Bessel functions.
Math. Comp. 25 (114), pp. 323–330.
-
Y. L. Luke (1972)
Miniaturized tables of Bessel functions. III.
Math. Comp. 26 (117), pp. 237–240 and A14–B5.
-
Y. L. Luke (1975)
Mathematical Functions and their Approximations.
Academic Press Inc., New York.
-
Y. L. Luke (1977a)
Algorithms for rational approximations for a confluent hypergeometric function.
Utilitas Math. 11, pp. 123–151.
-
Y. L. Luke (1977b)
Algorithms for the Computation of Mathematical Functions.
Academic Press, New York.
-
J. Lund (1985)
Bessel transforms and rational extrapolation.
Numer. Math. 47 (1), pp. 1–14.
-
J. H. Luscombe and M. Luban (1998)
Simplified recursive algorithm for Wigner and symbols.
Phys. Rev. E 57 (6), pp. 7274–7277.
-
W. Luther (1995)
Highly accurate tables for elementary functions.
BIT 35 (3), pp. 352–360.
-
R. J. Lyman and W. W. Edmonson (2001)
Linear prediction of bandlimited processes with flat spectral densities.
IEEE Trans. Signal Process. 49 (7), pp. 1564–1569.
-
A. E. Lynas-Gray (1993)
VOIGTL – A fast subroutine for Voigt function evaluation on vector processors.
Comput. Phys. Comm. 75 (1-2), pp. 135–142.
-
J. N. Lyness (1971)
Adjusted forms of the Fourier coefficient asymptotic expansion and applications in numerical quadrature.
Math. Comp. 25 (113), pp. 87–104.
-
J. N. Lyness (1985)
Integrating some infinite oscillating tails.
J. Comput. Appl. Math. 12/13, pp. 109–117.