On the evaluation of certain determinants
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- by Jean-L. Lavoie PDF
- Math. Comp. 18 (1964), 653-659 Request permission
Abstract:
Using the properties of the generalized Hilbert matrix and familiar results from the theory of hypergeometric series, we evaluate the determinants of certain matrices whose general terms are known explicitly. In certain cases it is even possible to find the analytic expression for the general terms of the inverses.References
- Earl D. Rainville, Special functions, The Macmillan Company, New York, 1960. MR 0107725
- Jean-L. Lavoie, On inverses of finite segments of the generalized Hilbert matrix, Math. Comp. 18 (1964), 141–143. MR 159832, DOI 10.1090/S0025-5718-1964-0159832-6
- G. Pólya and G. Szegö, Aufgaben und Lehrsätze aus der Analysis, Dover Publications, New York, N.Y., 1945 (German). MR 0015435
- A. R. Collar, On the reciprocal of a segment of a generalized Hilbert matrix, Proc. Cambridge Philos. Soc. 47 (1951), 11–17. MR 38325
- W. N. Bailey, On the sum of a terminating $_3F_2(1)$, Quart. J. Math. Oxford Ser. (2) 4 (1953), 237–240. MR 57381, DOI 10.1093/qmath/4.1.237
Additional Information
- © Copyright 1964 American Mathematical Society
- Journal: Math. Comp. 18 (1964), 653-659
- MSC: Primary 65.35
- DOI: https://doi.org/10.1090/S0025-5718-1964-0170465-8
- MathSciNet review: 0170465