Frank W. J. Olver
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Most Influential Person Now
American mathematician who worked on asymptotic analysis, special functions
Frank W. J. Olver's AcademicInfluence.com Rankings
Frank W. J. Olvermathematics Degrees
Mathematics
#4504
World Rank
#6385
Historical Rank
#1543
USA Rank
Measure Theory
#736
World Rank
#992
Historical Rank
#293
USA Rank
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Mathematics
Why Is Frank W. J. Olver Influential?
(Suggest an Edit or Addition)According to Wikipedia, Frank William John Olver was a professor of mathematics at the Institute for Physical Science and Technology and Department of Mathematics at the University of Maryland who worked on asymptotic analysis, special functions, and numerical analysis. He was the editor in chief of the NIST Digital Library of Mathematical Functions.
Frank W. J. Olver's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- Asymptotics and Special Functions (1974) (3865)
- NIST Handbook of Mathematical Functions (2010) (3680)
- Handbook for Automatic Computation (1960) (461)
- Introduction to Asymptotics and Special Functions (1974) (363)
- The asymptotic expansion of bessel functions of large order (1954) (323)
- Digital Library of Mathematical Functions (2003) (152)
- INTRODUCTION TO SPECIAL FUNCTIONS (1974) (146)
- The asymptotic solution of linear differential equations of the second order for large values of a parameter (1954) (139)
- The Special Functions and Their Approximations (Vols. I & II Yudell L. Luke) (1972) (129)
- Uniform asymptotic expansions for Weber parabolic cylinder functions of large orders (1959) (123)
- Numerical solution of second-order linear difference equations (1967) (117)
- Second-order linear differential equations with two turning points (1975) (96)
- Uniform, exponentially improved, asymptotic expansions for the generalized exponential integral (1991) (74)
- Error bounds for the Liouville–Green (or WKB) approximation (1961) (68)
- Error Bounds for Stationary Phase Approximations (1974) (67)
- A New Approach to Error Arithmetic (1978) (63)
- Note on backward recurrence algorithms (1972) (59)
- Why Steepest Descents (1970) (53)
- Some new asymptotic expansions for Bessel functions of large orders (1952) (51)
- The asymptotic solution of linear differential equations of the second order in a domain containing one transition point (1956) (44)
- Error analysis of Miller’s recurrence algorithm (1964) (42)
- INTRODUCTION TO ASYMPTOTIC ANALYSIS (1974) (42)
- Uniform asymptotic expansions of solutions of linear second-order differential equations for large values of a parameter (1958) (41)
- Airy and related functions (2010) (37)
- General connection formulae for Liouville-Green approximations in the complex plane (1978) (35)
- A further method for the evaluation of zeros of Bessel functions and some new asymptotic expansions for zeros of functions of large order (1951) (35)
- Associated legendre functions on the cut (1983) (34)
- The evaluation of zeros of high-degree polynomials (1952) (33)
- Connection Formulas for Second-Order Differential Equations with Multiple Turning Points (1977) (31)
- Extended-Range Arithmetic and Normalized Legendre Polynomials (1981) (31)
- Exponentially improved asymptotic solutions of ordinary differential equations. II. Irregular singularities of rank one (1994) (31)
- Level-Index Arithmetic: An Introductory Survey (1989) (30)
- Bessel Functions, Part III, Zeros and Associated Values. (1961) (28)
- Unsolved Problems in the Asymptotic Estimation of Special Functions (1975) (26)
- Level-index arithmetic operations (1987) (26)
- Whittaker functions with both parameters large: uniform approximations in terms of parabolic cylinder functions (1980) (25)
- On the Reversion of an Asymptotic Expansion and the Zeros of the Airy Functions (1999) (25)
- Sufficient Conditions for Ackerberg–O’Malley Resonance (1978) (24)
- Tables for Bessel Functions of Moderate or Large Orders (1963) (23)
- Closure and precision in level-index arithmetic (1990) (23)
- Bounds for the solutions of second-order linear difference equations (1967) (22)
- On the calculation of Stokes multipliers for linear differential equations of the second order (1995) (22)
- Legendre functions with both parameters large (1975) (22)
- Connection Formulas for Second-Order Differential Equations Having an Arbitrary Number of Turning Points of Arbitrary Multiplicities (1977) (22)
- A Posteriori Error Bounds for Gaussian Elimination (1982) (21)
- An Unrestricted Algorithm for the Exponential Function (1980) (21)
- On the Asymptotic Solution of Second-Order Differential Equations Having an Irregular Singularity of Rank One, with an Application to Whittaker Functions (1965) (20)
- Further Developments of Rp and Ap Error Analysis (1982) (20)
- Error Bounds for Asymptotic Expansions in Turning-Point Problems (1964) (20)
- On the Asymptotic and Numerical Solution of Linear Ordinary Differential Equations (1998) (20)
- Exponentially-improved asymptotic solutions of ordinary differential equations I: the confluent hypergeometric function (1993) (19)
- Implementation of level-index arithmetic using partial table look-up (1987) (19)
- Error Bounds for First Approximations in Turning-Point Problems (1963) (18)
- Asymptotic expansions of the coefficients in asymptotic series solutions of linear differential equations (1994) (17)
- A new method for the evaluation of zeros of Bessel functions and of other solutions of second-order differential equations (1950) (16)
- Error analysis of phase-integral methods .II. Application to wave-penetration problems (1965) (16)
- Computation of complex Airy functions and their zeros using asymptotics and the differential equation (2004) (15)
- Error bounds for the laplace approximation for definite integrals (1968) (15)
- Asymptotic Approximations and Error Bounds (1980) (15)
- Second-order differential equations with fractional transition points (1977) (14)
- Error Bounds for Asymptotic Solutions of Second-Order Differential Equations Having an Irregular Singularity of Arbitrary Rank (1965) (14)
- Error analysis of phase-integral methods. I. General theory for simple turning points (1965) (14)
- A Special Functions Handbook for the Digital Age (2011) (13)
- Error Bounds for Polynomial Evaluation and Complex Arithmetic (1986) (13)
- Airy and Bessel Functions by Parallel Integration of ODEs (1993) (13)
- Generalized exponential and logarithmic functions (1986) (12)
- Two inequalities for parabolic cylinder functions (1961) (12)
- Coulomb Wave Functions (1965) (12)
- The generalized exponential integral (1994) (11)
- Asymptotic approximations (2010) (11)
- ERROR ANALYSIS OF COMPLEX ARITHMETIC (1983) (11)
- Zeros and associated values (1960) (11)
- ERROR ANALYSIS OF COMPLEX ARITHMETIC (1983) (11)
- A closed computer arithmetic (1987) (9)
- The NIST Handbook of Mathematical Functions | NIST (2010) (9)
- Some results on co-recursive associated Laguerre and Jacobi polynomials (1994) (8)
- Error bounds for linear recurrence relations (1988) (7)
- Error Bounds for Arithmetic Operations on Computers Without Guard Digits (1983) (7)
- Improved error bounds for second-order differential equations with two turning points (1976) (7)
- Asymptotic and Computational Analysis: Conference in Honor of Frank W.j. Olver's 65th Birthday (2017) (7)
- RESURGENCE IN DIFFERENCE EQUATIONS, WITH AN APPLICATION TO LEGENDRE FUNCTIONS (2000) (7)
- Unrestricted algorithms for reciprocals and square roots (1986) (6)
- Asymptotic approximations for parabolic cylinder functions (1978) (4)
- A Paradox in Asymptotics (1970) (4)
- TRANSFORMATION OF CERTAIN SERIES OCCURRING IN AERODYNAMIC INTERFERENCE CALCULATIONS (1949) (4)
- Linear Differential Equations of the Second Order with a Large Parameter (1959) (4)
- The use of economized polynomials in mathematical tables (1955) (3)
- ASYMPTOTIC SOLUTIONS OF LINEAR ORDINARY DIFFERENTIAL EQUATIONS AT AN IRREGULAR SINGULARITY OF RANK UNITY (2016) (3)
- DIFFERENTIAL EQUATIONS WITH IRREGULAR SINGULARITIES; BESSEL AND CONFLUENT HYPERGEOMETRIC FUNCTIONS (1974) (3)
- DIFFERENTIAL EQUATIONS WITH A PARAMETER: TURNING POINTS (1974) (3)
- Notes on Numerical Analysis--3: Solution of Differential Equations by Recurrence Relations (1951) (2)
- Algebraic and analytic methods (2010) (2)
- Unrestricted Algorithms for Generating Elementary Functions (1980) (2)
- An extension of Miller's algorithm (1968) (2)
- Note on the Asymptotic Expansion of Generalized Hypergeometric Functions (1953) (2)
- On Stokes’ Phenomenon and Converging Factors (2020) (2)
- DIFFERENTIAL EQUATIONS WITH REGULAR SINGULARITIES; HYPERGEOMETRIC AND LEGENDRE FUNCTIONS (1974) (1)
- THE LIOUVILLE–GREEN APPROXIMATION (1974) (1)
- DIFFERENTIAL EQUATIONS WITH A PARAMETER: EXPANSIONS IN ELEMENTARY FUNCTIONS (1974) (1)
- The General Connection-Formula Problem for Linear Differential Equations of the Second Order (1980) (1)
- Note on a Paper of H. Bateman (1946) (1)
- RECENT ERROR ANALYSIS OF ASYMPTOTIC SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS (1975) (1)
- Asymptotics and Special Functions/ Frank W. J. Olver (1997) (1)
- ESTIMATION OF REMAINDER TERMS (1974) (0)
- 4 – CONTOUR INTEGRALS (1974) (0)
- Existence Theorems for Linear Differential Equations: Complex Variables (1997) (0)
- Ratio of Two Gamma Functions; Watson's Lemma for Loop Integrals (1997) (0)
- Review of Mathematical Function Library for Microsoft-FORTRAN, John Wiley & Sons, 1989 (1990) (0)
- Elementary functions (2010) (0)
- On the uniqueness of asymptotic solutions of linear differential equations (1999) (0)
- Errors in asymptotic solutions of linear ordinary differential equations (1956) (0)
- DIFFERENTIAL EQUATIONS WITH A PARAMETER: SIMPLE POLES AND OTHER TRANSITION POINTS (1974) (0)
- The Method of Stationary Phase (1997) (0)
- Linear Turning Point Theory (Wolfgang Wasow) (1986) (0)
- INTEGRALS: FURTHER METHODS (1974) (0)
- The Symbols ~, o, and 0 (1997) (0)
- The Hypergeometric Equation (1997) (0)
- CONNECTION FORMULAS FOR SOLUTIONS OF DIFFERENTIAL EQUATIONS (1974) (0)
- Selected papers of F.W.J. Olver (2000) (0)
- Error Analysis; Variational Operator (1997) (0)
- Algorithm xxx: Airy Functions (2004) (0)
- Origin of Asymptotic Expansions (1997) (0)
- SUMS AND SEQUENCES (1974) (0)
- Asymptotic Nature of the Stationary Phase Approximation (1997) (0)
- Bessel functions (2021) (0)
- Fundamental Research in Applied Mathematics. (1984) (0)
- Mathematics that has intrigued me (2014) (0)
- INTEGRALS OF A REAL VARIABLE (1974) (0)
- Computation of Complex Airy Functions and Zeros using Asymptotics and Differential Equation | NIST (2004) (0)
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