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Some theorems on Stirling-type pairs

Published online by Cambridge University Press:  20 January 2009

Leetsch C. Hsu
Leetsch C. Hsu
Affiliation:
Institute of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
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Abstract

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It is shown that an extended Schlömilch formula for Stirling-type pairs of numbers and the inversion formula of Lagrange are implied by each other. Also proved are some congruence relations modulo a prime number p(>2) associated with generalized Stirling numbers. The third result is concerned with the asymptotic expansions of Stirling-type pairs involving large parameters.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 36 , Issue 3 , October 1993 , pp. 525 - 535
Copyright
Copyright © Edinburgh Mathematical Society 1993

References

REFERENCES

1.Butzer, P. L. and Hauss, M., Stirling functions of the first and second kind; some new applications, Approximation, Interpolation and Summability (Proc. Conf. in honour of Prof. Jakimovski, Tel Aviv, 06 4–8, 1990, Research Institute of Math. Sciences, Bar Ilan Univ., Weizmann Press, Israel).Google Scholar
2.Butzer, P. L. and Hauss, M., On Stirling functions of the second kind, preprint from Lehrstuhl A für Mathematik, Aachen Univ. of Technology, 1989.Google Scholar
3.Butzer, P. L., Schmidt, M., Stark, E. L. and Vogt, L., Central factorial numbers; their main properties and some applications, Numer. Fund. Anal. Optim. 10 (1989), 419–488.CrossRefGoogle Scholar
4.Butzer, P. L., Markett, C. and Schmidt, M., Stirling numbers, central factorial numbers, and representations of the Riemann zeta function, preprint from Lehrstuhl A für Mathematik, Aachen Univ. of Technology, 1991.CrossRefGoogle Scholar
5.Comtet, L., Advanced Combinatorics (D. Reidel Publ. Company, Dordrecht, Holland, 1974).CrossRefGoogle Scholar
6.Hsu, L. C., Generalized Stirling number pairs associated with inverse relations, Fibonacci Quart. 25 (1987), 346–351.Google Scholar
7.Hsu, L. C., Theory and application of generalized Stirling number pairs, J. Math. Res. Exposition Quart. 9 (1989), 211–220.Google Scholar
8.Hsu, L. C. and Chu, W., A kind of asymptotic expansion using partitions, Tôhoku Math. J. 43 (1991), 235–242.CrossRefGoogle Scholar
9.Hsu, L. C., Note on an asymptotic expansion of the nth difference of zero, Ann Math. Stat. 19 (1948), 273–277.CrossRefGoogle Scholar
10.Jordan, C., Calculus of Finite Differences (Chelsea Publ. Company, New York, 1950).Google Scholar
11.Moser, L. and Wyman, M., Stirling numbers of the second kind, Duke Math. J. 25 (1958), 29–43.CrossRefGoogle Scholar