Bibliography O
-
F. Oberhettinger and T. P. Higgins (1961)
Tables of Lebedev, Mehler and Generalized Mehler Transforms,
Mathematical Note
Technical Report 246, Boeing Scientific Research Lab, Seattle.
-
F. Oberhettinger (1990)
Tables of Fourier Transforms and Fourier Transforms of Distributions,
Springer-Verlag, Berlin.
-
F. Oberhettinger and L. Badii (1973)
Tables of Laplace Transforms,
Springer-Verlag, Berlin-New York.
-
F. Oberhettinger (1972)
Tables of Bessel Transforms,
Springer-Verlag, Berlin-New York.
-
F. Oberhettinger (1973)
Fourier Expansions. A Collection of Formulas,
Academic Press, New York-London.
-
F. Oberhettinger (1974)
Tables of Mellin Transforms,
Springer-Verlag, Berlin-New York.
-
A. M. Odlyzko (1987)
On the distribution of spacings between zeros of the zeta function,
Math. Comp. 48 (177), pp. 273–308.
-
A. M. Odlyzko (1995)
Asymptotic Enumeration Methods,
in Handbook of Combinatorics, Vol. 2,
(R. L. Graham and M. Grötschel Eds.), pp. 1063–1229.
-
O. M. Ogreid and P. Osland (1998)
Summing one- and two-dimensional series related to the Euler series,
J. Comput. Appl. Math. 98 (2), pp. 245–271.
-
K. Okamoto (1981)
On the
-function of the Painlevé equations,
Phys. D 2 (3), pp. 525–535.
-
K. Okamoto (1986)
Studies on the Painlevé equations. III. Second and fourth Painlevé equations,
and 
,
Math. Ann. 275 (2), pp. 221–255.
-
K. Okamoto (1987a)
Studies on the Painlevé equations. I. Sixth Painlevé equation
,
Ann. Mat. Pura Appl. (4) 146, pp. 337–381.
-
K. Okamoto (1987b)
Studies on the Painlevé equations. II. Fifth Painlevé equation
,
Japan. J. Math. (N.S.) 13 (1), pp. 47–76.
-
K. Okamoto (1987c)
Studies on the Painlevé equations. IV. Third Painlevé equation
,
Funkcial. Ekvac. 30 (2-3), pp. 305–332.
-
S. Okui (1974)
Complete elliptic integrals resulting from infinite integrals of Bessel functions,
J. Res. Nat. Bur. Standards Sect. B 78B (3), pp. 113–135.
-
S. Okui (1975)
Complete elliptic integrals resulting from infinite integrals of Bessel functions. II,
J. Res. Nat. Bur. Standards Sect. B 79B (3-4), pp. 137–170.
-
A. B. Olde Daalhuis and F. W. J. Olver (1994)
Exponentially improved asymptotic solutions of ordinary differential equations. II Irregular singularities of rank one,
Proc. Roy. Soc. London Ser. A 445, pp. 39–56.
-
A. B. Olde Daalhuis and F. W. J. Olver (1995a)
Hyperasymptotic solutions of second-order linear differential equations. I,
Methods Appl. Anal. 2 (2), pp. 173–197.
-
A. B. Olde Daalhuis and F. W. J. Olver (1995b)
On the calculation of Stokes multipliers for linear differential equations of the second order,
Methods Appl. Anal. 2 (3), pp. 348–367.
-
A. B. Olde Daalhuis and F. W. J. Olver (1998)
On the asymptotic and numerical solution of linear ordinary differential equations,
SIAM Rev. 40 (3), pp. 463–495.
-
A. B. Olde Daalhuis and N. M. Temme (1994)
Uniform Airy-type expansions of integrals,
SIAM J. Math. Anal. 25 (2), pp. 304–321.
-
A. B. Olde Daalhuis (1994)
Asymptotic expansions for
-gamma, -exponential, and -Bessel functions,
J. Math. Anal. Appl. 186 (3), pp. 896–913.
-
A. B. Olde Daalhuis (1995)
Hyperasymptotic solutions of second-order linear differential equations. II,
Methods Appl. Anal. 2 (2), pp. 198–211.
-
A. B. Olde Daalhuis (1996)
Hyperterminants. I,
J. Comput. Appl. Math. 76 (1-2), pp. 255–264.
-
A. B. Olde Daalhuis (1998a)
Hyperasymptotic solutions of higher order linear differential equations with a singularity of rank one,
Proc. Roy. Soc. London Ser. A 454, pp. 1–29.
-
A. B. Olde Daalhuis (1998b)
Hyperterminants. II,
J. Comput. Appl. Math. 89 (1), pp. 87–95.
-
A. B. Olde Daalhuis (1998c)
On the resurgence properties of the uniform asymptotic expansion of the incomplete gamma function,
Methods Appl. Anal. 5 (4), pp. 425–438.
-
A. B. Olde Daalhuis (2000)
On the asymptotics for late coefficients in uniform asymptotic expansions of integrals with coalescing saddles,
Methods Appl. Anal. 7 (4), pp. 727–745.
-
A. B. Olde Daalhuis (2003a)
Uniform asymptotic expansions for hypergeometric functions with large parameters. I,
Analysis and Applications (Singapore) 1 (1), pp. 111–120.
-
A. B. Olde Daalhuis (2003b)
Uniform asymptotic expansions for hypergeometric functions with large parameters. II,
Analysis and Applications (Singapore) 1 (1), pp. 121–128.
-
A. B. Olde Daalhuis (2004a)
Inverse factorial-series solutions of difference equations,
Proc. Edinb. Math. Soc. (2) 47 (2), pp. 421–448.
-
A. B. Olde Daalhuis (2004b)
On higher-order Stokes phenomena of an inhomogeneous linear ordinary differential equation,
J. Comput. Appl. Math. 169 (1), pp. 235–246.
-
A. B. Olde Daalhuis (2005a)
Hyperasymptotics for nonlinear ODEs. I. A Riccati equation,
Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 461 (2060), pp. 2503–2520.
-
A. B. Olde Daalhuis (2005b)
Hyperasymptotics for nonlinear ODEs. II. The first Painlevé equation and a second-order Riccati equation,
Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 461 (2062), pp. 3005–3021.
-
A. B. Olde Daalhuis (2010)
Uniform asymptotic expansions for hypergeometric functions with large parameters. III,
Analysis and Applications (Singapore).
-
M. N. Olevskiĭ (1950)
Triorthogonal systems in spaces of constant curvature in which the equation
allows a complete separation of variables,
Mat. Sbornik N.S. 27(69) (3), pp. 379–426 (Russian).
-
T. Oliveira e Silva (2006)
Computing
: The combinatorial method,
Revista do DETUA 4 (6), pp. 759–768.
-
J. Oliver (1977)
An error analysis of the modified Clenshaw method for evaluating Chebyshev and Fourier series,
J. Inst. Math. Appl. 20 (3), pp. 379–391.
-
I. Olkin (1959)
A class of integral identities with matrix argument,
Duke Math. J. 26 (2), pp. 207–213.
-
F. W. J. Olver and J. M. Smith (1983)
Associated Legendre functions on the cut,
J. Comput. Phys. 51 (3), pp. 502–518.
-
F. W. J. Olver and D. J. Sookne (1972)
Note on backward recurrence algorithms,
Math. Comp. 26 (120), pp. 941–947.
-
F. W. J. Olver and F. Stenger (1965)
Error bounds for asymptotic solutions of second-order differential equations having an irregular singularity of arbitrary rank,
J. Soc. Indust. Appl. Math. Ser. B Numer. Anal. 2 (2), pp. 244–249.
-
F. W. J. Olver (1950)
A new method for the evaluation of zeros of Bessel functions and of other solutions of second-order differential equations,
Proc. Cambridge Philos. Soc. 46 (4), pp. 570–580.
-
F. W. J. Olver (1951)
A further method for the evaluation of zeros of Bessel functions and some new asymptotic expansions for zeros of functions of large order,
Proc. Cambridge Philos. Soc. 47, pp. 699–712.
-
F. W. J. Olver (1952)
Some new asymptotic expansions for Bessel functions of large orders,
Proc. Cambridge Philos. Soc. 48 (3), pp. 414–427.
-
F. W. J. Olver (1954)
The asymptotic expansion of Bessel functions of large order,
Philos. Trans. Roy. Soc. London. Ser. A. 247, pp. 328–368.
-
F. W. J. Olver (1959)
Uniform asymptotic expansions for Weber parabolic cylinder functions of large orders,
J. Res. Nat. Bur. Standards Sect. B 63B, pp. 131–169.
-
F. W. J. Olver (Ed.) (1960)
Bessel Functions. Part III: Zeros and Associated Values,
Royal Society Mathematical Tables, Volume 7, Cambridge University Press, Cambridge-New York.
-
F. W. J. Olver (1962)
Tables for Bessel Functions of Moderate or Large Orders,
National Physical Laboratory Mathematical Tables, Vol. 6.
Department of Scientific and Industrial Research, Her Majesty’s Stationery Office, London.
-
F. W. J. Olver (1964a)
Error analysis of Miller’s recurrence algorithm,
Math. Comp. 18 (85), pp. 65–74.
-
F. W. J. Olver (1964b)
Error bounds for asymptotic expansions in turning-point problems,
J. Soc. Indust. Appl. Math. 12 (1), pp. 200–214.
-
F. W. J. Olver (1965)
On the asymptotic solution of second-order differential equations having an irregular singularity of rank one, with an application to Whittaker functions,
J. Soc. Indust. Appl. Math. Ser. B Numer. Anal. 2 (2), pp. 225–243.
-
F. W. J. Olver (1967a)
Numerical solution of second-order linear difference equations,
J. Res. Nat. Bur. Standards Sect. B 71B, pp. 111–129.
-
F. W. J. Olver (1967b)
Bounds for the solutions of second-order linear difference equations,
J. Res. Nat. Bur. Standards Sect. B 71B (4), pp. 161–166.
-
F. W. J. Olver (1970)
A paradox in asymptotics,
SIAM J. Math. Anal. 1 (4), pp. 533–534.
-
F. W. J. Olver (1974)
Error bounds for stationary phase approximations,
SIAM J. Math. Anal. 5 (1), pp. 19–29.
-
F. W. J. Olver (1975a)
Second-order linear differential equations with two turning points,
Philos. Trans. Roy. Soc. London Ser. A 278, pp. 137–174.
-
F. W. J. Olver (1975b)
Legendre functions with both parameters large,
Philos. Trans. Roy. Soc. London Ser. A 278, pp. 175–185.
-
F. W. J. Olver (1976)
Improved error bounds for second-order differential equations with two turning points,
J. Res. Nat. Bur. Standards Sect. B 80B (4), pp. 437–440.
-
F. W. J. Olver (1977a)
Connection formulas for second-order differential equations with multiple turning points,
SIAM J. Math. Anal. 8 (1), pp. 127–154.
-
F. W. J. Olver (1977b)
Connection formulas for second-order differential equations having an arbitrary number of turning points of arbitrary multiplicities,
SIAM J. Math. Anal. 8 (4), pp. 673–700.
-
F. W. J. Olver (1977c)
Second-order differential equations with fractional transition points,
Trans. Amer. Math. Soc. 226, pp. 227–241.
-
F. W. J. Olver (1978)
General connection formulae for Liouville-Green approximations in the complex plane,
Philos. Trans. Roy. Soc. London Ser. A 289, pp. 501–548.
-
F. W. J. Olver (1980a)
Asymptotic approximations and error bounds,
SIAM Rev. 22 (2), pp. 188–203.
-
F. W. J. Olver (1980b)
Whittaker functions with both parameters large: Uniform approximations in terms of parabolic cylinder functions,
Proc. Roy. Soc. Edinburgh Sect. A 86 (3-4), pp. 213–234.
-
F. W. J. Olver (1983)
Error Analysis of Complex Arithmetic,
in Computational Aspects of Complex Analysis (Braunlage, 1982),
(L. Wuytack, E. Ng and H. J. Bünger Eds.), NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., Vol. 102, pp. 279–292.
-
F. W. J. Olver (1991a)
Uniform, exponentially improved, asymptotic expansions for the generalized exponential integral,
SIAM J. Math. Anal. 22 (5), pp. 1460–1474.
-
F. W. J. Olver (1991b)
Uniform, exponentially improved, asymptotic expansions for the confluent hypergeometric function and other integral transforms,
SIAM J. Math. Anal. 22 (5), pp. 1475–1489.
-
F. W. J. Olver (1993a)
Exponentially-improved asymptotic solutions of ordinary differential equations I: The confluent hypergeometric function,
SIAM J. Math. Anal. 24 (3), pp. 756–767.
-
F. W. J. Olver (1994a)
Asymptotic expansions of the coefficients in asymptotic series solutions of linear differential equations,
Methods Appl. Anal. 1 (1), pp. 1–13.
-
F. W. J. Olver (1994b)
The Generalized Exponential Integral,
in Approximation and Computation (West Lafayette, IN, 1993),
International Series of Numerical Mathematics, Vol. 119, pp. 497–510.
-
F. W. J. Olver (1995)
On an asymptotic expansion of a ratio of gamma functions,
Proc. Roy. Irish Acad. Sect. A 95 (1), pp. 5–9.
-
F. W. J. Olver (1997a)
Asymptotic solutions of linear ordinary differential equations at an irregular singularity of rank unity,
Methods Appl. Anal. 4 (4), pp. 375–403.
-
F. W. J. Olver (1997b)
Asymptotics and Special Functions,
A. K. Peters, Wellesley, MA.
-
F. W. J. Olver (1999)
On the uniqueness of asymptotic solutions of linear differential equations,
Methods Appl. Anal. 6 (2), pp. 165–174.
-
P. J. Olver (1993b)
Applications of Lie Groups to Differential Equations,
2nd edition, Graduate Texts in Mathematics, Vol. 107, Springer-Verlag, New York.
-
S. Olver (2011)
Numerical solution of Riemann-Hilbert problems: Painlevé II,
Found. Comput. Math. 11 (2), pp. 153–179.
-
On-Line Encyclopedia of Integer Sequences (Web Site)
AT&T Labs, Inc.–Research, Florham Park and Middletown, New Jersey..
-
M. K. Ong (1986)
A closed form solution of the
-wave Bethe-Goldstone equation with an infinite repulsive core,
J. Math. Phys. 27 (4), pp. 1154–1158.
-
K. Ono (2000)
Distribution of the partition function modulo
,
Ann. of Math. (2) 151 (1), pp. 293–307.
-
G. E. Ordóñez and D. J. Driebe (1996)
Spectral decomposition of tent maps using symmetry considerations,
J. Statist. Phys. 84 (1-2), pp. 269–276.
-
J. M. Ortega and W. C. Rheinboldt (1970)
Iterative Solution of Nonlinear Equations in Several Variables,
Academic Press, New York.
-
H. Oser (1960)
Algorithm 22: Riccati-Bessel functions of first and second kind,
Comm. ACM 3 (11), pp. 600–601.
-
A. M. Ostrowski (1973)
Solution of Equations in Euclidean and Banach Spaces,
Pure and Applied Mathematics, Vol. 9, Academic Press, New York-London.
-
C. Osácar, J. Palacián and M. Palacios (1995)
Numerical evaluation of the dilogarithm of complex argument,
Celestial Mech. Dynam. Astronom. 62 (1), pp. 93–98.
-
R. H. Ott (1985)
Scattering by a parabolic cylinder—a uniform asymptotic expansion,
J. Math. Phys. 26 (4), pp. 854–860.
-
M. L. Overton (2001)
Numerical Computing with IEEE Floating Point Arithmetic,
Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
