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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2015.1
- 수록면
- 103 - 107 (5page)
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We use some known contiguous function relations for ${}_2F_1$ toshow how simply the following three recurrence relations for Jacobi polynomials $P_n^{(\alpha,\beta)}(x)$:\begin{enumerate}\item[(i)] $(\alpha + \beta +n)\, P_n^{(\alpha,\beta)}(x)= (\beta +n)\, P_n^{(\alpha,\beta-1)}(x) + (\alpha + n)\, P_n^{(\alpha-1,\beta)}(x);$
\item[(ii)] $2\, P_n^{(\alpha,\beta)}(x)= (1+x)\, P_n^{(\alpha,\beta+1)}(x) + (1-x)\, P_n^{(\alpha+1,\beta)}(x);$
\item[(iii)] $ P_{n-1}^{(\alpha,\beta)}(x)= P_n^{(\alpha,\beta-1)}(x) + P_n^{(\alpha-1,\beta)}(x)$
\end{enumerate}can be established.
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