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# Mary Celine Fasenmyer

Sister Mary Celine Fasenmyer (October 4, 1906, Crown, Pennsylvania – December 27, 1996, Erie, Pennsylvania) was a mathematician. She is most noted for her work on hypergeometric functions and linear algebra.

Life

Sister Celine grew up in Pennsylvania's oil country and displayed mathematical talent in high school. For ten years after her graduation she taught and studied at Mercyhurst College in Erie, where she joined the Sisters of Mercy. She pursued her mathematical studies in Pittsburgh and the University of Michigan, obtaining her doctorate in 1946.

After getting her Ph.D., Sister Celine published two papers which expanded on her doctorate work. These papers would be further elaborated by Doron Zeilberger and Herbert Wilf into "WZ theory", which allowed computerized proof of many combinatorial identities. After this, she returned to Mercyhurst to teach and did not engage in further research.

Sister Celine's method

Sister Celine is most remembered for the method that bears her name, first elucidated 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.

Publications

* Some Generalized Hypergeometric Polynomials, Ph.D. thesis. University of Michigan, 1945.

* Some Generalized Hypergeometric Polynomials, Bull. Amer. Math. Soc. 53, 806–812, 1947.

* A Note on Pure Recurrence Relations, Amer. Math. Monthly 56, 14–17, 1949.

References

* Biography, primary source for this article

* Sister Celine's Methods, Theorems, and DemonstrationsPDF (251 KB)

* Weisstein, Eric W., "Sister Celine's Method" from MathWorld.

External links

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

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