单词 | Sister Celine's Method |
释义 | Sister Celine's MethodA method for finding Recurrence Relations for hypergeometric polynomials directly from theseries expansions of the polynomials. The method is effective and easily implemented, but usually slower thanZeilberger's Algorithm. Given a sum ![]() by proceeding as follows (Petkovsek et al. 1996, p. 59):
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Fasenmyer, Sister M. C. Some Generalized Hypergeometric Polynomials. Ph.D. thesis. University of Michigan, Nov. 1945. Fasenmyer, Sister M. C. ``Some Generalized Hypergeometric Polynomials.'' Bull. Amer. Math. Soc. 53, 806-812, 1947. Fasenmyer, Sister M. C. ``A Note on Pure Recurrence Relations.'' Amer. Math. Monthly 56, 14-17, 1949. Petkovsek, M.; Wilf, H. S.; and Zeilberger, D. ``Sister Celine's Method.'' Ch. 4 in A=B. Wellesley, MA: A. K. Peters, pp. 55-72, 1996. Rainville, E. D. Chs. 14 and 18 in Special Functions. New York: Chelsea, 1971. Verbaten, P. ``The Automatic Construction of Pure Recurrence Relations.'' Proc. EUROSAM '74, ACM-SIGSAM Bull. 8, 96-98, 1974. Wilf, H. S. and Zeilberger, D. ``An Algorithmic Proof Theory for Hypergeometric (Ordinary and `` |
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