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Journal article
The Stirling Numbers of the Second Kind and Their Applications
Alabama Journal of Mathematics: Official Journal of the ACTM and AACTM, Vol.47(1), pp.1-22
2024
Abstract
The Stirling numbers of the second kind have numerous applications in mathematics and statistics. But these applications are not generally known to college mathematics and statistics students. This paper aims to propagate the use of the Stirling Number of the second kind to college mathematics and statistics students. We approach the Stirling numbers of the second kind very lucidly so that college students can grasp them easily. We derive a formula for the Stirling numbers of the second kind using the concept of one-to-one and onto functions. Using this formula, we derive a recurrence relation. By
the multinomial theorem, we express a monomial rⁿ in terms of the Stirling numbers of the second kind and falling factorial of order r . Using this enerating function, we gave a closed form of the sums of integral powers of integers. Finally, as applications in statistics, we offer closed form for nth (raw) moments of a few discrete distributions such as Binomial, Poisson, Geometric, and Negative Binomial.
Details
- Title
- The Stirling Numbers of the Second Kind and Their Applications
- Publication Details
- Alabama Journal of Mathematics: Official Journal of the ACTM and AACTM, Vol.47(1), pp.1-22
- Resource Type
- Journal article
- Publisher
- Alabama Council of Teachers of Mathematics (ACTM) and the Alabama Association of College Teachers of Mathematics (AACTM)
- Copyright
- Permission granted to the University of West Florida Libraries by the author to digitize and/or display this information for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires the permission of the copyright holder.
- Identifiers
- 99381464573206600
- Academic Unit
- Mathematics and Statistics; Hal Marcus College of Science and Engineering
- Language
- English