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. Erie is the fifth largest city in Pennsylvania and the largest city in Northwestern Pennsylvania with a population of 94,831 a ...

) 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, structure, space, models, and change. History On ...

and

Catholic The Catholic Church, also known as the Roman Catholic Church, is the largest Christian church, with 1.3 billion baptized Catholics worldwide . It is among the world's oldest and largest international institutions, and has played a ...

religious

sister A sister is a woman or a girl who shares one or more parents 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 refer to ...

. She is most noted for her work on hypergeometric functions 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 matrices. ...

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

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Biography

Fasenmyer grew up in

Pennsylvania Pennsylvania (; ( Pennsylvania Dutch: )), officially the Commonwealth of Pennsylvania, is a state spanning the Mid-Atlantic, Northeastern, Appalachian, and Great Lakes regions of the United States. It borders Delaware to its southeast, ...

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

Mercyhurst College (Seize the day) , former_names = Mercyhurst College (1926–2012) , established = , type = Private university , religious_affiliation = Roman Catholic (Sisters of Mercy) , endowment = $31.8 million , faculty = 136 full-time , administra ...

Erie Erie (; ) is a city on the south shore of Lake Erie and the county seat of Erie County, Pennsylvania, United States. Erie is the fifth largest city in Pennsylvania and the largest city in Northwestern Pennsylvania with a population of 94,831 a ...

, where she joined the

Sisters of Mercy The Sisters of Mercy is a religious institute of Catholic women founded in 1831 in Dublin, Ireland, by Catherine McAuley. As of 2019, the institute had about 6200 sisters worldwide, organized into a number of independent congregations. They a ...

. She pursued her mathematical studies in Pittsburgh and the

University of Michigan , mottoeng = "Arts, Knowledge, Truth" , former_names = Catholepistemiad, or University of Michigania (1817–1821) , budget = $10.3 billion (2021) , endowment = $17 billion (2021)As o ...

, obtaining her

doctorate A doctorate (from Latin ''docere'', "to teach"), doctor's degree (from Latin ''doctor'', "teacher"), or doctoral degree is an academic degree awarded by universities and some other educational institutions, derived from the ancient formalism ''l ...

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 a university press affiliated with the Massachusetts Institute of Technology (MIT) in Cambridge, Massachusetts (United States). It was established in 1962. History The MIT Press traces its origins back to 1926 when MIT publish ...

. 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 (דורון ציילברגר, born 2 July 1950 in Haifa, Israel) is an Israeli mathematician, known for his work in combinatorics. Education and career He received his doctorate from the Weizmann Institute of Science in 1976, u ...

and

Herbert Wilf Herbert Saul Wilf (June 13, 1931 – January 7, 2012) was a mathematician, specializing in combinatorics and graph theory. He was the Thomas A. Scott Professor of Mathematics in Combinatorial Analysis and Computing at the University of Pennsylv ...

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 an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many app ...

. 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 In mathematics, Sister Celine's polynomials are a family of hypergeometric polynomials introduced by . They include Legendre polynomials, Jacobi polynomials, and Bateman polynomials In mathematics, the Bateman polynomials are a family ''F'n'' of o ...

References

Publications

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External links

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

Agnes Scott College Agnes Scott College is a private women's liberal arts college in Decatur, Georgia. The college enrolls approximately 1,000 undergraduate and graduate students. The college is affiliated with the Presbyterian Church and is considered one of the ...

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