Special Session: In Honor of Oleg Marichev on the Occasion of His 60th Birthday

Wolfram Technology Conference
Saturday, October 8, 2005, 8 a.m.-noon

• Stephen Wolfram: "The History and Future of Special Functions"
• Michael Trott: "The Wolfram Functions Site"
• Oleksandr Pavlyk: "Special Functions in Mathematica"
• Paul Abbott: "A User's Perspective on The Wolfram Functions Site"
• Daniel Lichtblau: "Symbolic Definite Integration"
• Victor Adamchik: "On Closed Form Derivatives"

About Oleg Marichev

Publications (.nb)

Oleg Igorevich Marichev was born on September 7, 1945 in Velikie Luki, Russia--a small town near Pskov. After moving to Minsk, Belarus, in 1949, he became interested in mathematics in the eighth grade when a teacher introduced him to the method of mathematical induction. Oleg soon became an avid participant in local mathematics olympiads, winning countless competitions and a prestigious academic gold medal while attending a special mathematics high school at Belarusian State University. Oleg continued his studies as a college student there, and was recommended to the postgraduate school in 1968.

He would go on to lead a prolific mathematics career marked by originality, rigor, and completeness. As a postgraduate, Oleg worked under the guidance of Professor Fedor Gakhov--famous for having solved the classic Riemann boundary value problem for analytic functions in closed form. Oleg quickly extended this research to discover that boundary value problems for mixed-type partial differential equations could be converted into singular integral equations solvable with Gakhov's Riemann boundary algorithms.

While engaged in thesis research, Oleg branched off to explore what would become a lifelong fascination with special functions. His interest in hypergeometric, Bessel J-, Legendre P-, Appell F-, and Meijer G-functions was piqued by Lucy Joan Slater's book Generalized Hypergeometric Functions, which helped him recognize beautiful new mathematical applications. Applying integral equations and special functions to the solutions of partial differential equations ultimately became his thesis, and Oleg defended his first Ph.D. in 1973.

Oleg capped his initial investigations into special functions with a series of authoritative monographs. The first was published in Russian in 1978 and then translated into English as the Handbook of Integral Transforms of Higher Transcendental Functions. It developed ideas first considered by C. S. Meijer in the 1940s and was characterized by Gakhov as "[without] parallel in Russian or foreign literature." The Handbook was an especially key text because it included the largest Meijer G-function table ever compiled. This considerable feat allowed most integrals tabulated in handbooks such as Gradshteyn and Ryzik's Tables of Integrals, Series, and Products to be immediately evaluated as particular cases of the Meijer G-function. The research would also serve to shape, in part, Oleg's fundamental role in the future development of Mathematica.

Immediately following the Handbook, Oleg embarked on an even larger mission to compile a set of integral tables more comprehensive than Gradshteyn and Ryzik's, evaluating and re-evaluating thousands of complicated integrals by hand. The result was the five-volume Integrals and Series that he co-authored over the next decade.

Through all this research, Oleg had hoped to automate the algorithm for evaluating integrals. He finally got his chance in 1980 with Ernst Krupnikov on the high-performance MIR computer in Novosibirsk. Together, they implemented integration using the convolution theorem with Meijer G-functions. Several years later, Oleg guided his former Ph.D. student Victor Adamchik toward building a prototype integration system in REDUCE.

In 1990, Oleg and Victor were invited to the United States to demonstrate the REDUCE program to Wolfram Research, where they remained to significantly expand Mathematica's Integrate command. Around this time, Oleg also defended a second Ph.D. in mathematics from Friedrich-Schiller-Universität in Jena, Germany. Between 1992-97, Oleg actively worked at Wolfram Research on symbolic integration and numerical evaluation of MeijerG--the most complicated of Mathematica's special functions.

Oleg's special functions research came to a head in 1997 when he teamed with fellow special functions expert Michael Trott to begin the ambitious project of describing and classifying all of Mathematica's mathematical functions through formulas, graphics, and interrelations. Though the original intent was to create a set of five posters, the material quickly dwarfed the available space. The project was moved online where it now resides as The Wolfram Functions Site, the world's most comprehensive collection of mathematical formulas.

The Wolfram Functions Site and its nearly 100,000 formulas and graphics are now a focal point of Oleg's lifelong labors in special functions research, allowing him to realize his dream of building a "super handbook" of formulas for special and elementary functions even more complete than Integrals and Series--implemented entirely in Mathematica.

Read about the Festschrift for Oleg Marichev.