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Author Young, Tzay Y.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©1967
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Abstract This paper discusses a set of polynomials, ${φ\textit{r}(\textit{s})},$ orthogonal over a discrete range, with binomial distribution, $\textit{b}(\textit{s};$ $\textit{n},$ $\textit{p}),$ as the weighting function. Two recurrence relations are derived. One expresses $φ\textit{r}$ in terms of $φ\textit{r}-1$ and $Δφ\textit{r}-1,$ while the other relates $φ\textit{r}$ with $φ\textit{r}-1$ and $φ\textit{r}-2.$ It is shown that these polynomials are solutions of a finite difference equation. Also considered are two special cases. The first is the set of Hermite polynomials derived as a limiting case of the binomial-weighted orthogonal polynomials. The second deals with the Poisson distribution used as the weighting function.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 1967-01-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 14
Issue Number 1
Page Count 8
Starting Page 120
Ending Page 127


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Source: ACM Digital Library