Mary Celine Fasenmyer, RSM (October 4, 1906, Crown, Pennsylvania – December 27, 1996,

Erie, Pennsylvania Erie is a city on the south shore of Lake Erie and the county seat of Erie County, Pennsylvania, United States. It is the List of municipalities in Pennsylvania, fifth-most populous city in Pennsylvania and the most populous in Northwestern Pen ...

) was an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

and

Catholic The Catholic Church (), also known as the Roman Catholic Church, is the List of Christian denominations by number of members, largest Christian church, with 1.27 to 1.41 billion baptized Catholics Catholic Church by country, worldwid ...

religious

sister A sister is a woman or a girl who shares parents or a parent with another individual; a female sibling. The male counterpart is a brother. Although the term typically refers to a familial relationship, it is sometimes used endearingly to ref ...

. She is most noted for her work on

hypergeometric function In mathematics, the Gaussian or ordinary hypergeometric function 2''F''1(''a'',''b'';''c'';''z'') is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases. It is ...

s and

linear algebra Linear algebra is the branch of mathematics concerning linear equations such as :a_1x_1+\cdots +a_nx_n=b, linear maps such as :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrix (mathemat ...

.Rosen, KH and Michaels, JG (2000) ''Handbook of Discrete and Combinatorial Mathematics'',

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Biography

Fasenmyer grew up in

Pennsylvania Pennsylvania, officially the Commonwealth of Pennsylvania, is a U.S. state, state spanning the Mid-Atlantic (United States), Mid-Atlantic, Northeastern United States, Northeastern, Appalachian, and Great Lakes region, Great Lakes regions o ...

's oil country, and displayed mathematical talent in high school. For ten years after her graduation she taught and studied at

Mercyhurst College Mercyhurst University is a private Catholic university in Erie, Pennsylvania, United States. History On September 20, 1926, Mercyhurst College opened its doors just a few blocks away from the city's southern boundary. It was founded by the Si ...

Erie Erie is a city on the south shore of Lake Erie and the county seat of Erie County, Pennsylvania, United States. It is the fifth-most populous city in Pennsylvania and the most populous in Northwestern Pennsylvania with a population of 94,831 ...

, where she joined the

Sisters of Mercy The Sisters of Mercy is a religious institute for women in the Catholic Church. It was founded in 1831 in Dublin, Ireland, by Catherine McAuley. In 2019, the institute had about 6,200 Religious sister, sisters worldwide, organized into a number ...

. She pursued her mathematical studies in Pittsburgh and the

University of Michigan The University of Michigan (U-M, U of M, or Michigan) is a public university, public research university in Ann Arbor, Michigan, United States. Founded in 1817, it is the oldest institution of higher education in the state. The University of Mi ...

, obtaining her

doctorate A doctorate (from Latin ''doctor'', meaning "teacher") or doctoral degree is a postgraduate academic degree awarded by universities and some other educational institutions, derived from the ancient formalism '' licentia docendi'' ("licence to teach ...

in 1946 under the direction of Earl Rainville, with a dissertation entitled ''Some Generalized Hypergeometric Polynomials''.Murray, MAM (2001) ''Women Becoming Mathematicians: Creating a Professional Identity in Post-World War II America'',

MIT Press The MIT Press is the university press of the Massachusetts Institute of Technology (MIT), a private research university in Cambridge, Massachusetts. The MIT Press publishes a number of academic journals and has been a pioneer in the Open Ac ...

. After earning her Ph.D., Fasenmyer published two papers which expanded on her doctorate work. These would be further elaborated by

Doron Zeilberger Doron Zeilberger (; born 2 July 1950) is an Israeli-American mathematician, known for his work in combinatorics. Education and career He received his doctorate from the Weizmann Institute of Science in 1976, under the direction of Harry Dym, w ...

and

Herbert Wilf Herbert Saul Wilf (June 13, 1931 – January 7, 2012) was an American mathematician, specializing in combinatorics and graph theory. He was the Thomas A. Scott Professorship of Mathematics, Thomas A. Scott Professor of Mathematics in Combinatori ...

into "

WZ theory WZ may refer to: * WZ sex-determination system, also known as the ZW sex-determination system * WZ theory, a technique for simplifying certain combinatorial summations in mathematics * Eswatini (FIPS 10-4 country code WZ) * ''Westdeutsche Zeitung' ...

", which allowed computerized proof of many

combinatorial identities Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ap ...

. After this, she returned to Mercyhurst to teach and did not engage in further research. Fasenmyer died in 1996.

"Sister Celine's" method

Fasenmyer is most remembered for the method that bears her name, first described in her Ph.D. thesis concerning recurrence relations in hypergeometric series. The thesis demonstrated a purely algorithmic method to find recurrence relations satisfied by sums of terms of a hypergeometric polynomial, and requires only the series expansions of the polynomial. The beauty of her method is that it lends itself readily to computer automation. The work of Wilf and Zeilberger generalized the algorithm and established its correctness. The hypergeometric polynomials she studied are called Sister Celine's polynomials.

References

Publications

* *

External links

* * * *
Herbert Wilf and Lily Yen talk to Sister Celine (1993)
*

Agnes Scott College Agnes Scott College is a Private university, private Women's Colleges in the Southern United States, women's Liberal arts colleges in the United States, liberal arts college in Decatur, Georgia. The college enrolls approximately 1,000 undergra ...

{{DEFAULTSORT:Fasenmyer, Mary Celine 1906 births 1996 deaths 20th-century American educators 20th-century American mathematicians 20th-century American Roman Catholic nuns American mathematical analysts Mercyhurst University alumni People from Erie, Pennsylvania Sisters of Mercy Horace H. Rackham School of Graduate Studies alumni Catholics from Pennsylvania 20th-century American women mathematicians 20th-century American women educators