Special Session: In Honor of Oleg Marichev on the Occasion of His
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
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
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-Universitšt 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
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
Read about the Festschrift for Oleg Marichev.