Bibliography M
-
H. Maass (1971)
Siegel’s modular forms and Dirichlet series.
Lecture Notes in Mathematics, Vol. 216, Springer-Verlag, Berlin.
-
D. A. MacDonald (1989)
The roots of .
Quart. Appl. Math. 47 (2), pp. 375–378.
-
D. A. MacDonald (1997)
On the computation of zeroes of .
Quart. Appl. Math. 55 (4), pp. 623–633.
-
I. G. Macdonald (1972)
Affine root systems and Dedekind’s -function.
Invent. Math. 15 (2), pp. 91–143.
-
I. G. Macdonald (1982)
Some conjectures for root systems.
SIAM J. Math. Anal. 13 (6), pp. 988–1007.
-
I. G. Macdonald (1990)
Hypergeometric Functions.
-
I. G. Macdonald (1995)
Symmetric Functions and Hall Polynomials.
2nd edition, The Clarendon Press, Oxford University Press, New York-Oxford.
-
I. G. Macdonald (1998)
Symmetric Functions and Orthogonal Polynomials.
University Lecture Series, Vol. 12, American Mathematical Society, Providence, RI.
-
I. G. Macdonald (2000)
Orthogonal polynomials associated with root systems.
Sém. Lothar. Combin. 45, pp. Art. B45a, 40 pp. (electronic).
-
I. G. Macdonald (2003)
Affine Hecke Algebras and Orthogonal Polynomials.
Cambridge Tracts in Mathematics, Vol. 157, Cambridge University Press, Cambridge.
-
I. D. Macdonald (1968)
The Theory of Groups.
Clarendon Press, Oxford.
-
R. L. Mace and M. A. Hellberg (1995)
A dispersion function for plasmas containing superthermal particles.
Physics of Plasmas 2 (6), pp. 2098–2109.
-
N. W. Macfadyen and P. Winternitz (1971)
Crossing symmetric expansions of physical scattering amplitudes: The group and Lamé functions.
J. Mathematical Phys. 12, pp. 281–293.
-
A. J. MacLeod (1989)
Algorithm AS 245. A robust and reliable algorithm for the logarithm of the gamma function.
Appl. Statist. 38 (2), pp. 397–402.
-
A. J. MacLeod (1993)
Chebyshev expansions for modified Struve and related functions.
Math. Comp. 60 (202), pp. 735–747.
-
A. J. MacLeod (1994)
Computation of inhomogeneous Airy functions.
J. Comput. Appl. Math. 53 (1), pp. 109–116.
-
A. J. MacLeod (1996a)
Algorithm 757: MISCFUN, a software package to compute uncommon special functions.
ACM Trans. Math. Software 22 (3), pp. 288–301.
-
A. J. MacLeod (1996b)
Rational approximations, software and test methods for sine and cosine integrals.
Numer. Algorithms 12 (3-4), pp. 259–272.
-
A. J. MacLeod (1998)
Algorithm 779: Fermi-Dirac functions of order , , , .
ACM Trans. Math. Software 24 (1), pp. 1–12.
-
A. J. MacLeod (2002a)
Asymptotic expansions for the zeros of certain special functions.
J. Comput. Appl. Math. 145 (2), pp. 261–267.
-
A. J. MacLeod (2002b)
The efficient computation of some generalised exponential integrals.
J. Comput. Appl. Math. 148 (2), pp. 363–374.
-
T. M. MacRobert (1967)
Spherical Harmonics. An Elementary Treatise on Harmonic Functions with Applications.
3rd edition, International Series of Monographs in Pure and Applied Mathematics, Vol. 98, Pergamon Press, Oxford.
-
Magma (website)
Computational Algebra Group, School of Mathematics and Statistics, University of Sydney, Australia.
-
A. P. Magnus (1995)
Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials.
J. Comput. Appl. Math. 57 (1-2), pp. 215–237.
-
W. Magnus, F. Oberhettinger, and R. P. Soni (1966)
Formulas and Theorems for the Special Functions of Mathematical Physics.
3rd edition, Springer-Verlag, New York-Berlin.
-
W. Magnus and S. Winkler (1966)
Hill’s Equation.
Interscience Tracts in Pure and Applied Mathematics, No. 20, Interscience Publishers John Wiley & Sons, New York-London-Sydney.
-
W. Magnus (1941)
Zur Theorie des zylindrisch-parabolischen Spiegels.
Z. Physik 118, pp. 343–356 (German).
-
K. Mahler (1930)
Über die Nullstellen der unvollständigen Gammafunktionen.
Rend. del Circ. Matem. Palermo 54, pp. 1–41.
-
R. S. Maier (2005)
On reducing the Heun equation to the hypergeometric equation.
J. Differential Equations 213 (1), pp. 171–203.
-
R. S. Maier (2007)
The 192 solutions of the Heun equation.
Math. Comp. 76 (258), pp. 811–843.
-
H. Majima, K. Matsumoto, and N. Takayama (2000)
Quadratic relations for confluent hypergeometric functions.
Tohoku Math. J. (2) 52 (4), pp. 489–513.
-
K. L. Majumder and G. P. Bhattacharjee (1973)
Algorithm AS 63. The incomplete beta integral.
Appl. Statist. 22 (3), pp. 409–411.
-
S. Makinouchi (1966)
Zeros of Bessel functions and accurate to twenty-nine significant digits.
Technology Reports of the Osaka University 16 (685), pp. 1–44.
-
Yu. I. Manin (1998)
Sixth Painlevé Equation, Universal Elliptic Curve, and Mirror of .
In Geometry of Differential Equations, A. Khovanskii, A. Varchenko, and V. Vassiliev (Eds.),
Amer. Math. Soc. Transl. Ser. 2, Vol. 186, pp. 131–151.
-
E. L. Mansfield and H. N. Webster (1998)
On one-parameter families of Painlevé III.
Stud. Appl. Math. 101 (3), pp. 321–341.
-
Maple (commercial interactive system)
Maplesoft.
-
F. Marcellán, M. Alfaro, and M. L. Rezola (1993)
Orthogonal polynomials on Sobolev spaces: Old and new directions.
J. Comput. Appl. Math. 48 (1-2), pp. 113–131.
-
M. Marden (1966)
Geometry of Polynomials.
2nd edition, American Mathematical Society, Providence, RI.
-
O. I. Marichev (1983)
Handbook of Integral Transforms of Higher Transcendental Functions: Theory and Algorithmic Tables.
Ellis Horwood Ltd./John Wiley & Sons, Inc, Chichester/New York.
-
O. I. Marichev (1984)
On the Representation of Meijer’s -Function in the Vicinity of Singular Unity.
In Complex Analysis and Applications ’81 (Varna, 1981),
pp. 383–398.
-
B. Markman (1965)
Contribution no. 14. The Riemann zeta function.
BIT 5, pp. 138–141.
-
S. M. Markov (1981)
On the interval computation of elementary functions.
C. R. Acad. Bulgare Sci. 34 (3), pp. 319–322.
-
A. I. Markushevich (1983)
The Theory of Analytic Functions: A Brief Course.
“Mir”, Moscow.
-
A. I. Markushevich (1985)
Theory of Functions of a Complex Variable. Vols. I, II, III.
Chelsea Publishing Co., New York (English).
-
A. I. Markushevich (1992)
Introduction to the Classical Theory of Abelian Functions.
American Mathematical Society, Providence, RI.
-
P. Maroni (1995)
An integral representation for the Bessel form.
J. Comput. Appl. Math. 57 (1-2), pp. 251–260.
-
J. E. Marsden and A. J. Tromba (1996)
Vector Calculus.
4th edition, W. H. Freeman & Company, New York.
-
P. L. Marston (1992)
Geometrical and Catastrophe Optics Methods in Scattering.
In Physical Acoustics, A. D. Pierce and R. N. Thurston (Eds.),
Vol. 21, pp. 1–234.
-
P. L. Marston (1999)
Catastrophe optics of spheroidal drops and generalized rainbows.
J. Quantit. Spec. and Rad. Trans. 63, pp. 341–351.
-
B. Martić (1978)
Note sur certaines inégalités d’intégrales.
Akad. Nauka Umjet. Bosne Hercegov. Rad. Odjelj. Prirod. Mat.
Nauka 61 (17), pp. 165–168 (French, Serbo-Croatian summary).
-
P. Martín, R. Pérez, and A. L. Guerrero (1992)
Two-point quasi-fractional approximations to the Airy function .
J. Comput. Phys. 99 (2), pp. 337–340.
-
J. Martinek, H. P. Thielman, and E. C. Huebschman (1966)
On the zeros of cross-product Bessel functions.
J. Math. Mech. 16, pp. 447–452.
-
J. C. Mason and D. C. Handscomb (2003)
Chebyshev Polynomials.
Chapman & Hall/CRC, Boca Raton, FL.
-
J. C. Mason (1993)
Chebyshev polynomials of the second, third and fourth kinds in approximation, indefinite integration, and integral transforms.
In Proceedings of the Seventh Spanish Symposium on
Orthogonal Polynomials and Applications (VII SPOA)
(Granada, 1991),
Vol. 49, pp. 169–178.
-
D. R. Masson (1991)
Associated Wilson polynomials.
Constr. Approx. 7 (4), pp. 521–534.
-
T. Masuda, Y. Ohta, and K. Kajiwara (2002)
A determinant formula for a class of rational solutions of Painlevé V equation.
Nagoya Math. J. 168, pp. 1–25.
-
T. Masuda (2003)
On a class of algebraic solutions to the Painlevé VI equation, its determinant formula and coalescence cascade.
Funkcial. Ekvac. 46 (1), pp. 121–171.
-
T. Masuda (2004)
Classical transcendental solutions of the Painlevé equations and their degeneration.
Tohoku Math. J. (2) 56 (4), pp. 467–490.
-
A. M. Mathai (1993)
A Handbook of Generalized Special Functions for Statistical and Physical Sciences.
Oxford Science Publications, The Clarendon Press Oxford University Press, New York.
-
Mathematica (commercial interactive system)
Wolfram Research, Inc..
-
Matlab (commercial interactive system)
The MathWorks, Inc..
-
F. Matta and A. Reichel (1971)
Uniform computation of the error function and other related functions.
Math. Comp. 25 (114), pp. 339–344.
-
D. W. Matula and P. Kornerup (1980)
Foundations of Finite Precision Rational Arithmetic.
In Fundamentals of Numerical Computation (Computer-oriented
Numerical Analysis), G. Alefeld and R. D. Grigorieff (Eds.),
Comput. Suppl., Vol. 2, Vienna, pp. 85–111.
-
G. Matviyenko (1993)
On the evaluation of Bessel functions.
Appl. Comput. Harmon. Anal. 1 (1), pp. 116–135.
-
Maxima (free interactive system)
-
L. C. Maximon (1955)
On the evaluation of indefinite integrals involving the special functions: Application of method.
Quart. Appl. Math. 13, pp. 84–93.
-
L. C. Maximon (1991)
On the evaluation of the integral over the product of two spherical Bessel functions.
J. Math. Phys. 32 (3), pp. 642–648.
-
L. C. Maximon (2003)
The dilogarithm function for complex argument.
Proc. Roy. Soc. London Ser. A 459, pp. 2807–2819.
-
M. Mazzocco (2001a)
Rational solutions of the Painlevé VI equation.
J. Phys. A 34 (11), pp. 2281–2294.
-
M. Mazzocco (2001b)
Picard and Chazy solutions to the Painlevé VI equation.
Math. Ann. 321 (1), pp. 157–195.
-
R. C. McCann (1977)
Inequalities for the zeros of Bessel functions.
SIAM J. Math. Anal. 8 (1), pp. 166–170.
-
J. P. McClure and R. Wong (1978)
Explicit error terms for asymptotic expansions of Stieltjes transforms.
J. Inst. Math. Appl. 22 (2), pp. 129–145.
-
J. P. McClure and R. Wong (1979)
Exact remainders for asymptotic expansions of fractional integrals.
J. Inst. Math. Appl. 24 (2), pp. 139–147.
-
J. P. McClure and R. Wong (1987)
Asymptotic expansion of a multiple integral.
SIAM J. Math. Anal. 18 (6), pp. 1630–1637.
-
B. M. McCoy, C. A. Tracy, and T. T. Wu (1977)
Painlevé functions of the third kind.
J. Mathematical Phys. 18 (5), pp. 1058–1092.
-
B. M. McCoy (1992)
Spin Systems, Statistical Mechanics and Painlevé Functions.
In Painlevé Transcendents: Their Asymptotics and Physical Applications, D. Levi and P. Winternitz (Eds.),
NATO Adv. Sci. Inst. Ser. B Phys., Vol. 278, pp. 377–391.
-
F. A. McDonald and J. Nuttall (1969)
Complex-energy method for elastic -H scattering above the ionization threshold.
Phys. Rev. Lett. 23 (7), pp. 361–363.
-
J. N. McDonald and N. A. Weiss (1999)
A Course in Real Analysis.
Academic Press Inc., San Diego, CA.
-
H. R. McFarland and D. St. P. Richards (2001)
Exact misclassification probabilities for plug-in normal quadratic discriminant functions. I. The equal-means case.
J. Multivariate Anal. 77 (1), pp. 21–53.
-
H. R. McFarland and D. St. P. Richards (2002)
Exact misclassification probabilities for plug-in normal quadratic discriminant functions. II. The heterogeneous case.
J. Multivariate Anal. 82 (2), pp. 299–330.
-
H. McKean and V. Moll (1999)
Elliptic Curves.
Cambridge University Press, Cambridge.
-
N. M. McLachlan and A. L. Meyers (1936)
The ster and stei functions.
Phil. Mag. Series 7 21 (140), pp. 425–436.
-
N. W. McLachlan (1934)
Loud Speakers: Theory, Performance, Testing and Design.
Oxford University Press, New York.
-
N. W. McLachlan (1947)
Theory and Application of Mathieu Functions.
Clarendon Press, Oxford.
-
N. W. McLachlan (1961)
Bessel Functions for Engineers.
2nd edition, Clarendon Press, Oxford.
-
J. McMahon (1894)
On the roots of the Bessel and certain related functions.
Ann. of Math. 9 (1-6), pp. 23–30.
-
J. M. McNamee (2007)
Numerical Methods for Roots of Polynomials. Part I.
Studies in Computational Mathematics, Vol. 14, Elsevier, Amsterdam.
-
Fr. Mechel (1966)
Calculation of the modified Bessel functions of the second kind with complex argument.
Math. Comp. 20 (95), pp. 407–412.
-
V. Meden and K. Schönhammer (1992)
Spectral functions for the Tomonaga-Luttinger model.
Phys. Rev. B 46 (24), pp. 15753–15760.
-
D. S. Meek and D. J. Walton (1992)
Clothoid spline transition spirals.
Math. Comp. 59 (199), pp. 117–133.
-
R. Mehrem, J. T. Londergan, and M. H. Macfarlane (1991)
Analytic expressions for integrals of products of spherical Bessel functions.
J. Phys. A 24 (7), pp. 1435–1453.
-
M. L. Mehta (2004)
Random Matrices.
3rd edition, Pure and Applied Mathematics (Amsterdam), Vol. 142, Elsevier/Academic Press, Amsterdam.
-
C. S. Meijer (1946)
On the -function. VII, VIII.
Nederl. Akad. Wetensch., Proc. 49, pp. 1063–1072, 1165–1175 = Indagationes Math. 8, 661–670, 713–723 (1946).
-
J. W. Meijer and N. H. G. Baken (1987)
The exponential integral distribution.
Statist. Probab. Lett. 5 (3), pp. 209–211.
-
G. Meinardus (1967)
Approximation of Functions: Theory and Numerical Methods.
Springer Tracts in Natural Philosophy, Vol. 13, Springer-Verlag, New York.
-
P. N. Meisinger, T. R. Miller, and M. C. Ogilvie (2002)
Phenomenological equations of state for the quark-gluon plasma.
Phys. Rev. D 65 (3), pp. (034009–1)–(034009–10).
-
J. Meixner, F. W. Schäfke, and G. Wolf (1980)
Mathieu Functions and Spheroidal Functions and Their Mathematical Foundations: Further Studies.
Lecture Notes in Mathematics, Vol. 837, Springer-Verlag, Berlin-New York.
-
J. Meixner and F. W. Schäfke (1954)
Mathieusche Funktionen und Sphäroidfunktionen mit Anwendungen auf physikalische und technische Probleme.
Die Grundlehren der mathematischen Wissenschaften in
Einzeldarstellungen mit besonderer Berücksichtigung der
Anwendungsgebiete, Band LXXI, Springer-Verlag, Berlin (German).
-
J. Meixner (1951)
Klassifikation, Bezeichnung und Eigenschaften der Sphäroidfunktionen.
Math. Nachr. 5, pp. 1–18 (German).
-
J. Meixner (1944)
Die Laméschen Wellenfunktionen des Drehellipsoids.
Forschungsbericht No. 1952
ZWB (German).
-
A. J. Menezes, P. C. van Oorschot, and S. A. Vanstone (1997)
Handbook of Applied Cryptography.
CRC Press, Boca Raton, FL.
-
A. McD. Mercer (1992)
The zeros of as functions of order.
Internat. J. Math. Math. Sci. 15 (2), pp. 319–322.
-
J. N. Merner (1962)
Algorithm 149: Complete elliptic integral.
Comm. ACM 5 (12), pp. 605.
-
X. Merrheim (1994)
The computation of elementary functions in radix .
Computing 53 (3-4), pp. 219–232.
-
A. Messiah (1961)
Quantum Mechanics. Vol. I.
North-Holland Publishing Co., Amsterdam.
-
Meta.Numerics (website)
David Wright’s software package for .NET programming language
-
R. Metzler, J. Klafter, and J. Jortner (1999)
Hierarchies and logarithmic oscillations in the temporal relaxation patterns of proteins and other complex systems.
Proc. Nat. Acad. Sci. U .S. A. 96 (20), pp. 11085–11089.
-
A. Michaeli (1996)
Asymptotic analysis of edge-excited currents on a convex face of a perfectly conducting wedge under overlapping penumbra region conditions.
IEEE Trans. Antennas and Propagation 44 (1), pp. 97–101.
-
N. Michel and M. V. Stoitsov (2008)
Fast computation of the Gauss hypergeometric function with all its parameters complex with application to the Pöschl-Teller-Ginocchio potential wave functions.
Comput. Phys. Comm. 178 (7), pp. 535–551.
-
N. Michel (2007)
Precise Coulomb wave functions for a wide range of complex , and .
Computer Physics Communications 176 (3), pp. 232–249.
-
C. Micu and E. Papp (2005)
Applying -Laguerre polynomials to the derivation of -deformed energies of oscillator and Coulomb systems.
Romanian Reports in Physics 57 (1), pp. 25–34.
-
M. Micu (1968)
Recursion relations for the - symbols.
Nuclear Physics A 113 (1), pp. 215–220.
-
P. Midy (1975)
An improved calculation of the general elliptic integral of the second kind in the neighbourhood of .
Numer. Math. 25 (1), pp. 99–101.
-
G. J. Miel (1981)
Evaluation of complex logarithms and related functions.
SIAM J. Numer. Anal. 18 (4), pp. 744–750.
-
J. W. Miles (1978)
On the second Painlevé transcendent.
Proc. Roy. Soc. London Ser. A 361, pp. 277–291.
-
J. W. Miles (1975)
Asymptotic approximations for prolate spheroidal wave functions.
Studies in Appl. Math. 54 (4), pp. 315–349.
-
J. W. Miles (1980)
The Second Painlevé Transcendent: A Nonlinear Airy Function.
In Mechanics Today,
Vol. 5, pp. 297–313.
-
M. S. Milgram (1985)
The generalized integro-exponential function.
Math. Comp. 44 (170), pp. 443–458.
-
A. R. Miller and R. B. Paris (2011)
Euler-type transformations for the generalized hypergeometric function .
Z. Angew. Math. Phys. 62 (1), pp. 31–45.
-
A. R. Miller (1997)
A class of generalized hypergeometric summations.
J. Comput. Appl. Math. 87 (1), pp. 79–85.
-
A. R. Miller (2003)
On a Kummer-type transformation for the generalized hypergeometric function .
J. Comput. Appl. Math. 157 (2), pp. 507–509.
-
G. F. Miller (1960)
Tables of Generalized Exponential Integrals.
NPL Mathematical Tables, Vol. III, Her Majesty’s Stationery Office, London.
-
G. F. Miller (1966)
On the convergence of the Chebyshev series for functions possessing a singularity in the range of representation.
SIAM J. Numer. Anal. 3 (3), pp. 390–409.
-
J. C. P. Miller (1946)
The Airy Integral, Giving Tables of Solutions of the Differential Equation .
British Association for the Advancement of Science,
Mathematical Tables Part-Vol. B, Cambridge University Press, Cambridge.
-
J. C. P. Miller (1950)
On the choice of standard solutions for a homogeneous linear differential equation of the second order.
Quart. J. Mech. Appl. Math. 3 (2), pp. 225–235.
-
J. C. P. Miller (1952)
On the choice of standard solutions to Weber’s equation.
Proc. Cambridge Philos. Soc. 48, pp. 428–435.
-
J. C. P. Miller (Ed.) (1955)
Tables of Weber Parabolic Cylinder Functions.
Her Majesty’s Stationery Office, London.
-
J. Miller and V. S. Adamchik (1998)
Derivatives of the Hurwitz zeta function for rational arguments.
J. Comput. Appl. Math. 100 (2), pp. 201–206.
-
K. S. Miller and B. Ross (1993)
An Introduction to the Fractional Calculus and Fractional Differential Equations.
A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York.
-
W. Miller (1974)
Lie theory and separation of variables. I: Parabolic cylinder coordinates.
SIAM J. Math. Anal. 5 (4), pp. 626–643.
-
W. Miller (1977)
Symmetry and Separation of Variables.
Addison-Wesley Publishing Co., Reading, MA-London-Amsterdam.
-
J. P. Mills (1926)
Table of the ratio: Area to bounding ordinate, for any portion of normal curve.
Biometrika 18, pp. 395–400.
-
A. E. Milne, P. A. Clarkson, and A. P. Bassom (1997)
Bäcklund transformations and solution hierarchies for the third Painlevé equation.
Stud. Appl. Math. 98 (2), pp. 139–194.
-
S. C. Milne (1985a)
A -analog of the summation theorem for hypergeometric series well-poised in .
Adv. in Math. 57 (1), pp. 14–33.
-
S. C. Milne (1985b)
An elementary proof of the Macdonald identities for .
Adv. in Math. 57 (1), pp. 34–70.
-
S. C. Milne (1985c)
A new symmetry related to for classical basic hypergeometric series.
Adv. in Math. 57 (1), pp. 71–90.
-
S. C. Milne (1985d)
A -analog of hypergeometric series well-poised in and invariant -functions.
Adv. in Math. 58 (1), pp. 1–60.
-
S. C. Milne (1988)
A -analog of the Gauss summation theorem for hypergeometric series in .
Adv. in Math. 72 (1), pp. 59–131.
-
S. C. Milne (1994)
A -analog of a Whipple’s transformation for hypergeometric series in .
Adv. Math. 108 (1), pp. 1–76.
-
S. C. Milne (2002)
Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions.
Ramanujan J. 6 (1), pp. 7–149.
-
S. C. Milne and G. M. Lilly (1992)
The and Bailey transform and lemma.
Bull. Amer. Math. Soc. (N.S.) 26 (2), pp. 258–263.
-
S. C. Milne (1996)
New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function.
Proc. Nat. Acad. Sci. U.S.A. 93 (26), pp. 15004–15008.
-
S. C. Milne (1997)
Balanced summation theorems for basic hypergeometric series.
Adv. Math. 131 (1), pp. 93–187.
-
L. M. Milne-Thomson (1933)
The Calculus of Finite Differences.
Macmillan and Co. Ltd., London.
-
L. M. Milne-Thomson (1950)
Jacobian Elliptic Function Tables.
Dover Publications Inc., New York.
-
A. C. G. Mitchell and M. W. Zemansky (1961)
Resonance Radiation and Excited Atoms.
2nd edition, Cambridge Univerity Press, Cambridge, England.
-
D. S. Mitrinović (1964)
Elementary Inequalities.
P. Noordhoff Ltd., Groningen.
-
D. S. Mitrinović (1970)
Analytic Inequalities.
Springer-Verlag, New York.
-
D. S. Moak (1981)
The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
-
D. S. Moak (1984)
The -analogue of Stirling’s formula.
Rocky Mountain J. Math. 14 (2), pp. 403–413.
-
S. Moch, P. Uwer, and S. Weinzierl (2002)
Nested sums, expansion of transcendental functions, and multiscale multiloop integrals.
J. Math. Phys. 43 (6), pp. 3363–3386.
-
V. P. Modenov and A. V. Filonov (1986)
Calculation of zeros of cylindrical functions and their derivatives.
Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet. (2), pp. 63–64, 71 (Russian).
-
N. Mohankumar and A. Natarajan (1997)
The accurate evaluation of a particular Fermi-Dirac integral.
Comput. Phys. Comm. 101 (1-2), pp. 47–53.
-
E. W. Montroll (1964)
Lattice Statistics.
In Applied Combinatorial Mathematics, E. F. Beckenbach (Ed.),
University of California Engineering and Physical Sciences
Extension Series, pp. 96–143.
-
P. Moon and D. E. Spencer (1971)
Field Theory Handbook. Including Coordinate Systems, Differential Equations and Their Solutions.
2nd edition, Springer-Verlag, Berlin.
-
R. J. Moore (1982)
Algorithm AS 187. Derivatives of the incomplete gamma integral.
Appl. Statist. 31 (3), pp. 330–335.
-
R. E. Moore (1979)
Methods and Applications of Interval Analysis.
SIAM Studies in Applied Mathematics, Vol. 2, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
-
L. J. Mordell (1917)
On the representation of numbers as a sum of squares.
Quarterly Journal of Math. 48, pp. 93–104.
-
L. J. Mordell (1958)
On the evaluation of some multiple series.
J. London Math. Soc. (2) 33, pp. 368–371.
-
G. W. Morgenthaler and H. Reismann (1963)
Zeros of first derivatives of Bessel functions of the first kind, , , .
J. Res. Nat. Bur. Standards Sect. B 67B (3), pp. 181–183.
-
T. Morita (2013)
A connection formula for the -confluent hypergeometric function.
SIGMA Symmetry Integrability Geom. Methods Appl. 9, pp. Paper 050, 13.
-
T. Morita (1978)
Calculation of the complete elliptic integrals with complex modulus.
Numer. Math. 29 (2), pp. 233–236.
-
J. Morris (1969)
Algorithm 346: F-test probabilities [S14].
Comm. ACM 12 (3), pp. 184–185.
-
R. Morris (1979)
The dilogarithm function of a real argument.
Math. Comp. 33 (146), pp. 778–787.
-
P. M. Morse and H. Feshbach (1953a)
Methods of Theoretical Physics.
Vol. 1, McGraw-Hill Book Co., New York.
-
P. M. Morse and H. Feshbach (1953b)
Methods of Theoretical Physics.
Vol. 2, McGraw-Hill Book Co., New York.
-
C. Mortici (2011a)
A new Stirling series as continued fraction.
Numer. Algorithms 56 (1), pp. 17–26.
-
C. Mortici (2011b)
New sharp bounds for gamma and digamma functions.
An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 57 (1), pp. 57–60.
-
C. Mortici (2013a)
A continued fraction approximation of the gamma function.
J. Math. Anal. Appl. 402 (2), pp. 405–410.
-
C. Mortici (2013b)
Further improvements of some double inequalities for bounding the gamma function.
Math. Comput. Modelling 57 (5-6), pp. 1360–1363.
-
L. Moser and M. Wyman (1958a)
Asymptotic development of the Stirling numbers of the first kind.
J. London Math. Soc. 33, pp. 133–146.
-
L. Moser and M. Wyman (1958b)
Stirling numbers of the second kind.
Duke Math. J. 25 (1), pp. 29–43.
-
S. L. B. Moshier (1989)
Methods and Programs for Mathematical Functions.
Ellis Horwood Ltd., Chichester.
-
N. F. Mott and H. S. W. Massey (1956)
Theory of Atomic Collisions.
3rd edition, Oxford Univ. Press., Oxford.
-
MPFR (free C library)
-
mpmath (free python library)
-
R. J. Muirhead (1978)
Latent roots and matrix variates: A review of some asymptotic results.
Ann. Statist. 6 (1), pp. 5–33.
-
R. J. Muirhead (1982)
Aspects of Multivariate Statistical Theory.
John Wiley & Sons Inc., New York.
-
M. E. Muldoon and R. Spigler (1984)
Some remarks on zeros of cylinder functions.
SIAM J. Math. Anal. 15 (6), pp. 1231–1233.
-
M. E. Muldoon (1970)
Singular integrals whose kernels involve certain Sturm-Liouville functions. I.
J. Math. Mech. 19 (10), pp. 855–873.
-
M. E. Muldoon (1977)
Higher monotonicity properties of certain Sturm-Liouville functions. V.
Proc. Roy. Soc. Edinburgh Sect. A 77 (1-2), pp. 23–37.
-
M. E. Muldoon (1979)
On the zeros of a cross-product of Bessel functions of different orders.
Z. Angew. Math. Mech. 59 (6), pp. 272–273.
-
M. E. Muldoon (1981)
The variation with respect to order of zeros of Bessel functions.
Rend. Sem. Mat. Univ. Politec. Torino 39 (2), pp. 15–25.
-
H. P. Mulholland and S. Goldstein (1929)
The characteristic numbers of the Mathieu equation with purely imaginary parameter.
Phil. Mag. Series 7 8 (53), pp. 834–840.
-
D. Müller, B. G. Kelly, and J. J. O’Brien (1994)
Spheroidal eigenfunctions of the tidal equation.
Phys. Rev. Lett. 73 (11), pp. 1557–1560.
-
H. J. W. Müller (1962)
Asymptotic expansions of oblate spheroidal wave functions and their characteristic numbers.
J. Reine Angew. Math. 211, pp. 33–47.
-
H. J. W. Müller (1963)
Asymptotic expansions of prolate spheroidal wave functions and their characteristic numbers.
J. Reine Angew. Math. 212, pp. 26–48.
-
H. J. W. Müller (1966a)
Asymptotic expansions of ellipsoidal wave functions and their characteristic numbers.
Math. Nachr. 31, pp. 89–101.
-
H. J. W. Müller (1966b)
Asymptotic expansions of ellipsoidal wave functions in terms of Hermite functions.
Math. Nachr. 32, pp. 49–62.
-
H. J. W. Müller (1966c)
On asymptotic expansions of ellipsoidal wave functions.
Math. Nachr. 32, pp. 157–172.
-
J. Muller (1997)
Elementary Functions: Algorithms and Implementation.
Birkhäuser Boston Inc., Boston, MA.
-
K. H. Müller (1988)
Elastodynamics in parabolic cylinders.
Z. Angew. Math. Phys. 39 (5), pp. 748–752.
-
D. Mumford (1983)
Tata Lectures on Theta. I.
Birkhäuser Boston Inc., Boston, MA.
-
D. Mumford (1984)
Tata Lectures on Theta. II.
Birkhäuser Boston Inc., Boston, MA.
-
MuPAD (commercial interactive system and Matlab toolbox)
SciFace Software, Paderborn, Germany.
-
Y. Murata (1985)
Rational solutions of the second and the fourth Painlevé equations.
Funkcial. Ekvac. 28 (1), pp. 1–32.
-
Y. Murata (1995)
Classical solutions of the third Painlevé equation.
Nagoya Math. J. 139, pp. 37–65.
-
L. A. Muraveĭ (1976)
Zeros of the function .
Differential Equations 11, pp. 797–811.
-
B. T. M. Murphy and A. D. Wood (1997)
Hyperasymptotic solutions of second-order ordinary differential equations with a singularity of arbitrary integer rank.
Methods Appl. Anal. 4 (3), pp. 250–260.
-
J. Murzewski and A. Sowa (1972)
Tables of the functions of the parabolic cylinder for negative integer parameters.
Zastos. Mat. 13, pp. 261–273.
-
L. Mutafchiev and E. Kamenov (2006)
Asymptotic formula for the number of plane partitions of positive integers.
C. R. Acad. Bulgare Sci. 59 (4), pp. 361–366.