PUBLICATIONS IN JOURNALS

Note on a paper by H. Bateman, J. Appl. Phys. 17 (1946), 1127.

Transformation of certain series occurring in aerodynamic interference calculations, Quart. J. Mech. Appl. Math. 2 (1949), 452-457.

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 (1950), 570-580.

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 (1951), 699-712.

Solution of differential equations by recurrence relations, Math. Tab. Wash. (now Math. Comp.) 5 (1951), 34-39. (With C. W. Clenshaw.)

The evaluation of zeros of high-degree polynomials, Philos. Trans. Roy. Soc. London Ser. A 244 (1952), 385-415.

Some new asymptotic expansions for Bessel functions of large orders, Proc. Cambridge Philos. Soc. 48 (1952), 414-427.

Note on the asymptotic expansion of generalized hypergeometric functions, J. London Math. Soc. 28 (1953), 462-464.

The asymptotic solution of linear differential equations of the second order for large values of a parameter, Philos. Trans. Roy. Soc. London Ser. A 247 (1954), 307-327.

The asymptotic expansion of Bessel functions of large order, Philos. Trans. Roy. Soc. London Ser. A 247 (1954),328-368.

The use of economized polynomials in mathematical tables, Proc. Cambridge Philos. Soc. 51 (1955), 614-628. (With C. W. Clenshaw.)

The asymptotic solution of linear differential equations of the second order in a domain containing one transition point, Philos. Trans. Roy. Soc. London Ser. A 249 (1956), 65-97.

Errors in asymptotic solutions of linear ordinary differential equations, Quart. Appl. Math. 14 (1956), 218-219.

Uniform asymptotic expansions of solutions of linear second-order differential equations for large values of a parameter, Philos. Trans. Roy. Soc. London Ser. A 250 (1958), 479-517.

Linear differential equations of the second order with a large parameter, J. Soc. Indust. and Appl. Math. 7 (1959), 306-310.

Uniform asymptotic expansions for Weber parabolic cylinder functions of large orders, J. Res. Nat. Bur. Standards 63B (1959), 131-169.

Error bounds for the Liouville-Green (or WKB) approximation, Proc. Cambridge Philos. Soc. 57 (1961), 790-810.

Two inequalities for parabolic cylinder functions, Proc. Cambridge Philos. Soc. 57 (1961), 811-822.

Error bounds for first approximations in turning-point problems, J. Soc. Indust. and Appl. Math. 11 (1963), 748-772.

Error bounds for asymptotic expansions in turning-point problems, J. Soc. Indust. and Appl. Math. 12 (1964), 200-214.

Error analysis of Miller's recurrence algorithm, Math. Comp. 18 (1964), 65-74.

On the asymptotic solutions 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 2 (1965), 225-243.

Error bounds for asymptotic solutions of second-order differential equations having an irregular singularity of arbitrary rank, J. Soc. Indust. Appl. Math., Ser. B 2 (1965), 244-249. (With F. Stenger.)

Error analysis of phase-integral methods. I. General theory for simple turning points, J. Res. Nat. Bur. Standards 69B (1965), 271-290.

Error analysis of phase-integral methods. II. Application to wave-penetration problems, J. Res. Nat. Bur. Standards 69B (1965), 291-300.

Numerical solution of second-order linear difference equations, J. Res. Nat. Bur. Standards 71B (1967), 111-129.

Bounds for the solutions of second-order linear difference equations, J. Res. Nat. Bur. Standards 71B (1967), 161-166.

An extension of Miller's algorithm, Apl. Mat. No. 2, 13 (1968), 174-176.

Error bounds for the Laplace approximation for definite integrals, J. Approx. Theory 1 (1968), 293-313.

Why steepest descents? SIAM Rev. 12 (1970), 228-247. Reprinted in Special Functions and Wave Propagation, Studies in Applied Mathematics 6 (D. Ludwig and F.W.J. Olver, eds.), Society for Industrial and Applied Mathematics, Philadelphia, PA, 1970, pp. 44-63.

A paradox in asymptotics, SIAM J. Math. Anal. 1 (1970), 533-534.

Note on backward recurrence algorithms, Math. Comp. 26 (1972), 941-947. (With D. J. Sookne.)

Error bounds for stationary phase approximations, SIAM J. Math. Anal. 5 (1974), 19-29.

Second-order linear differential equations with two turning points, Philos. Trans. Roy. Soc. London Ser. A 278 (1975), 137-174.

Legendre functions with both parameters large, Philos. Trans. Roy. Soc. London Ser. A 278 (1975), 175-185.

Improved error bounds for second-order differential equations with two turning points, J. Res. Nat. Bur. Standards 80B (1976), 437-440.

Second-order differential equations with fractional transition points, Trans. Amer. Math. Soc. 226 (1977), 227-241.

Connection formulas for second-order differential equations with multiple turning points, SIAM J. Math. Anal. 8 (1977), 127-154.

Connection formulas for second-order differential equations having an arbitrary number of turning points of arbitrary multiplicities, SIAM J. Math. Anal. 8 (1977), 673-700.

Asymptotic behavior of integrals of Bessel functions of high order, Utilitas Math. 12 (1977), 225-239. (With M. L. Glasser.)

A new approach to error arithmetic, SIAM J. Numer. Anal. 15 (1978), 368-393.

Sufficient conditions for Ackerberg-O'Malley resonance, SIAM J. Math. Anal. 9 (1978), 328-355.

General connection formulae for Liouville-Green approximations in the complex plane, Philos. Trans. Roy. Soc. London Ser. A 289 (1978), 501-548.

Asymptotic approximations for parabolic cylinder functions, J. Phys. B: Atom. Molec. Phys. 11 (1978), L531-L533. (With C. Lozano.)

An unrestricted algorithm for the exponential function, SIAM J. Numer. Anal. 17 (1980), 310-331. (With C. W. Clenshaw.)

Asymptotic approximations and error bounds, SIAM Rev. 22 (1980), 188-203.

Whittaker functions with both parameters large; uniform approximations in terms of parabolic cylinder functions, Proc. Roy. Soc. Edinburgh Sect. A 86 (1980), 213-234.

Extended-range arithmetic and normalized Legendre polynomials, ACM Trans. Math. Software 7 (1981), 93-105. (With J. M. Smith and D. W. Lozier.)

Further developments of rp and ap error analysis, IMA J. Numer. Anal. 2 (1982), 249-274.

A posteriori error bounds for Gaussian elimination, IMA J. Numer. Anal. 2 (1982), 377-406. (With J. H. Wilkinson.)

Associated Legendre functions on the cut, J. Comput. Phys. 51 (1983), 502-518. (With J. M. Smith.)

Error bounds for arithmetic operations on computers without guard digits, IMA J. Numer. Anal. 3 (1983), 153-160.

Beyond floating point, J. Assoc. Comput. Mach. 31 (1984), 319-328. (With C. W. Clenshaw.)

Error bounds for polynomial evaluation and complex arithmetic, IMA J. Numer. Anal. 6 (1986), 373-379.

Generalized exponential and logarithmic functions, Comput. Math. Appl. 12B (1986), 1091-1101. (With C. W. Clenshaw, D. W. Lozier and P. R. Turner.)

Unrestricted algorithms for reciprocals and square roots, BIT 26 (1986), 476-492. (With C. W. Clenshaw.)

Level-index arithmetic operations, SIAM J. Numer. Anal. 24 (1987), 470-485. (With C. W. Clenshaw.)

Error bounds for linear recurrence relations, Math. Comp. 50 (1988), 481-499.

Closure and precision in level-index arithmetic, SIAM J. Numer. Anal. 27 (1990), 1295-1304. (With D. W. Lozier.)

Uniform, exponentially improved, asymptotic expansions for the generalized exponential integral, SIAM J. Math. Anal. 22 (1991), 1460-1474.

Uniform, exponentially improved, asymptotic expansions for the confluent hypergeometric function and other integral transforms, SIAM J. Math. Anal. 22 (1991), 1475-1489.

Exponentially-improved asymptotic solutions of ordinary differential equations I: The confluent hypergeometric function, SIAM J. Math. Anal. 24 (1993), 756-767.

Asymptotic expansions of the coefficients in asymptotic series solutions of linear differential equations, Methods Appl. Anal. 1 (1994), 1-13.

Exponentially improved asymptotic solutions of ordinary differential equations. II Irregular singularities of rank one, Proc. Roy. Soc. London Ser. A 445 (1994), 39-56. (With A. B. Olde Daalhuis.)

On an asymptotic expansion of a ratio of Gamma functions, Proc. Roy. Irish Academy Sect. A 95 (1995), 5-9.

Hyperasymptotic solutions of second-order linear differential equations I, Methods Appl. Anal. 2 (1995), 173-197. (With A.B. Olde Daalhuis.)

On the calculation of Stokes multipliers for linear differential equations of the second order, Methods Appl. Anal. 2 (1995), 348-367. (With A. B. Olde Daalhuis.)

Asymptotic solutions of linear ordinary differential equations at an irregular singularity of rank unity, Methods Appl. Anal. 4 (1997), 375-403.

On the asymptotic and numerical solution of linear ordinary differential equations, SIAM Rev. 40 (1998), 463-495. (With A. B. Olde Daalhuis.)

On the uniqueness of asymptotic solutions of linear differential equations, Methods Appl. Anal. 6 (1999), 165-174.

Special Issue of the SIAM Journal on Mathematical Analysis, dedicated to Richard A. Askey and Frank W J. Olver, 25, no. 2, March 1994, pp. 243-814.

 

Updated 6/24/09