# Obituaries: Frank W.J. Olver, 1924-2013

Born in 1924 in Croydon, UK, Frank showed deep interest in mathematics and proved himself a mathematical talent at a young age. He received a bachelor’s degree with first-class honors in mathematics from the University of London in 1944, followed by a master’s degree in 1948 and a DSc in mathematical analysis in 1961. At the age of 19, on completion of his undergraduate studies, Frank was assigned to the British Admiralty Computing Service, where he was introduced to numerical analysis. It was at that time that his research interest in special functions began to take shape.

Frank later joined the National Physical Laboratory, where he became a founding member of the Mathematics Division. NPL turned out to be a milestone in his career and life. There, his work in compiling numerical tables of zeros of Bessel functions marked the beginning of his life-long interest in asymptotics and special functions. There too, he met his first wife, Grace. They were married in 1948 and had three children, Peter, Linda, and Sally.

Frank was invited to spend the year 1957–58 at the National Bureau of Standards (now the National Institute of Standards and Technology) in Washington, DC, where he wrote “Bessel Functions of Integer Order,” a chapter for the *Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables*, edited by Milton Abramowitz and Irene Stegun. When he returned to NPL, it was with an open invitation to work at NBS; persuaded by Grace to accept, Frank moved to the U.S. in 1961 and spent the rest of his life there. In 1969, he joined the University of Maryland as research professor; on his retirement, in 1992, he was appointed professor emeritus.

Frank wrote numerous papers on asymptotics, numerical analysis, and special functions, and served on the editorial boards of several leading journals in mathematical and numerical analysis. Very active in SIAM, he was one of the founders of *SIAM Journal on Mathematical Analysis* and its first managing editor, from 1970 to 1975. His first book, *Asymptotics and Special Functions*, published in 1974 by Academic Press, became a standard reference in those fields. It was translated into Russian in 1990 and reprinted in 1997.

Among his many contributions, one that could be lauded as his “lifetime achievement” was his involvement, as editor-in-chief and mathematics editor, in the *NIST Handbook of Mathematical Functions* and its web counterpart, the *NIST Digital Library of Mathematical Functions* (DLMF), both published in 2010. This daunting task took Frank, together with editorial and production staff at NIST and about 50 international authors and validators, 10 years to complete. The new publications continued the legacy of their predecessor, the Handbook edited by Abramowitz and Stegun, as an authoritative publication on special functions. The DLMF project, under his leadership, earned the group of nine NIST contributors the Gold Medal of the U.S. Department of Commerce; DLMF was also chosen as one of 10 Government Computer News Award Winners for “Outstanding Information Technology Achievement in Government.”

In addition to his important contributions to mathematics, Frank’s seriousness about accuracy earned him great respect and appreciation. Everyone who worked with him, read his work, or knew him personally will agree that he was meticulous and precise. When proofreading, he would read every formula backward to ensure that no error was missed. For the book *Asymptotics and Special Functions*, after reading all the galley proofs and page proofs, he traveled to New York to proofread the final manuscript before printing. “He is amazing,” says his son Peter, a mathematician at the University of Minnesota. “I don’t know any other mathematician who has paid that much attention to detail.”

As editor of the NIST Handbook, Frank went through every single chapter and every single line several times, whether the text had been written by him or by other scholars. He read each chapter eight or nine times to pick up even the most minor errors, always refining the language to make it as perfect as possible. Leonard Maximon of George Washington University, an associate editor of the project who worked closely with Frank, once said that Frank’s “commitment to assuring that the NIST Handbook was as perfect and coherent a work as is possible involved a Herculean task; I know of no one else that could have accomplished it.”

In the mid-1950s, Frank wrote a series of papers on what is now known as uniform asymptotic expansions that appeared in the *Philosophical Transactions of the Royal Society of London* [4–7]; the papers caught the attention of mathematicians who were working in asymptotic analysis as well as of applied mathematicians who were using asymptotics for their applied problems. In the early 1960s, Frank began to work on the construction of numerical bounds for truncation errors associated with asymptotic expansions. Among existing bounds, those provided by Frank still seem to be most realistic and computable.

Although known largely for his work in asymptotic analysis, Frank also made substantial contributions to numerical analysis. In fact, many of his early papers were either on the numerical computation of special functions or on error analysis of recurrence algorithms (e.g., [8,9]). In the late 1970s and early 80s, Frank returned to numerical analysis, constructing with Jim Wilkinson [10] a posteriori error bounds for Gaussian elimination, and proposing with Charlie Clenshaw [2,3] a new number system for computer arithmetic, which they called the level-index system. In 1989, in an important paper [1] that presented a new interpretation of the Stokes phenomenon, Sir Michael Berry adopted the view that the change in form of a compound asymptotic expansion occurs smoothly, although very rapidly, as a Stokes line is crossed. Berry’s argument is based on R.D. Dingle’s theory of terminants, and is hence quite formal. In a series of papers, Frank developed new analysis to place the theories of Dingle and Berry on rigorous mathematical foundations.

In 2000, commemorating Frank’s impressive contributions to mathematics, a two-volume collection of his selected papers was published. The 1074-page collection consists of 56 papers covering his most important contributions in the areas of asymptotic analysis, special functions, and numerical analysis, during the years from 1949 to 1999.

Frank will be remembered as one of the great mathematicians of our time, for his profound influence on the development of special functions, as an editor admirable for his attention to details, and as an inspiring scholar for the standards and references he created for succeeding generations of mathematicians.

Frank is survived by his second wife, Claire, his brother, Terence, son Peter and daughter Sally, their spouses, Cheri and Neal, and five grandchildren, Parizad, Krista, Sheehan, Brian, and Noreen.

**References **

[1] M.V. Berry, *Uniform asymptotic smoothing of Stokes’ discontinuities*, Proc. R. Soc. A, 422 (1989), 7–21.

[2] C.W. Clenshaw and F.W.J. Olver, *Beyond floating point*, J. Assoc. Comput. Mach., 31 (1984), 319–328.

[3] C.W. Clenshaw and F.W.J. Olver, *Level-index arithmetic operations*, SIAM J. Numer. Anal., 24 (1987), 470–485.

[4] F.W.J. Olver, *The asymptotic solution of linear differential equations of the second order for large values of a parameter*, Phil. Trans. R. Soc. A, 247 (1954), 307–327.

[5] F.W.J. Olver, *The asymptotic expansion of Bessel functions of large order*, Phil. Trans. R. Soc. A, 247 (1954), 328–368.

[6] F.W.J. Olver, *The asymptotic solution of linear differential equations of the second order in a domain containing one transition point*, Phil. Trans. R. Soc. A, 249 (1956), 65–97.

[7] F.W.J. Olver, *Uniform asymptotic expansions of solutions of linear second-order differential equations for large values of a parameter*, Phil. Trans. R. Soc. A, 250 (1958), 479–517.

[8] F.W.J. Olver, *Numerical solution of second-order linear difference equations*, J. Res. Nat. Bur. Standards, 71B (1967), 111–129.

[9] F.W.J. Olver, *Bounds for the solutions of second-order linear difference equations*, J. Res. Nat. Bur. Standards, 71B (1967), 161–166.

[10] F.W.J. Olver and J.H. Wilkinson, *A posteriori error bounds for Gaussian elimination*, IMA J. Numer. Anal., 2 (1982), 377–406.