셀베르그 적분(Selberg integral)
이 항목의 스프링노트 원문주소셀베르그 적분==
개요==
- 오일러 베타적분의 일반화
\(\begin{align} S_{n} (\alpha, \beta, \gamma) & = \int_0^1 \cdots \int_0^1 \prod_{i=1}^n t_i^{\alpha-1}(1-t_i)^{\beta-1} \prod_{1 \le i < j \le n} |t_i - t_j |^{2 \gamma}\,dt_1 \cdots dt_n = \\ & = \prod_{j = 0}^{n-1} \frac {\Gamma(\alpha + j \gamma) \Gamma(\beta + j \gamma) \Gamma (1 + (j+1)\gamma)} {\Gamma(\alpha + \beta + (n+j-1)\gamma) \Gamma(1+\gamma)} \end{align}\)
- n=1 인 경우
\(S_{1} (\alpha, \beta,\gamma)=B(\alpha,\beta) = \int_0^1t^{\alpha-1}(1-t)^{\beta-1}\,dt\)
\(\begin{align} S_{n} (\alpha, \beta, \gamma) & = \int_0^1 \cdots \int_0^1 \prod_{i=1}^n t_i^{\alpha-1}(1-t_i)^{\beta-1} \prod_{1 \le i < j \le n} |t_i - t_j |^{2 \gamma}\,dt_1 \cdots dt_n = \\ & = \prod_{j = 0}^{n-1} \frac {\Gamma(\alpha + j \gamma) \Gamma(\beta + j \gamma) \Gamma (1 + (j+1)\gamma)} {\Gamma(\alpha + \beta + (n+j-1)\gamma) \Gamma(1+\gamma)} \end{align}\)
\(S_{1} (\alpha, \beta,\gamma)=B(\alpha,\beta) = \int_0^1t^{\alpha-1}(1-t)^{\beta-1}\,dt\)
재미있는 사실==
역사==
메모==
관련된 항목들==
수학용어번역==
사전 형태의 자료==
관련논문==
- On a Selberg–Schur Integral
- Sergio Manuel Iguri, 2009
- Beta Integrals
- S. Ole Warnaar
- The importance of the Selberg integral
- Peter J. Forrester; S. Ole Warnaar, Bull. Amer. Math. Soc. 45 (2008), 489-534.
- Hankel hyperdeterminants and Selberg integrals
- J.-G. Luque, J.-Y. Thibon, 2002
- Sergio Manuel Iguri, 2009
- S. Ole Warnaar
- Peter J. Forrester; S. Ole Warnaar, Bull. Amer. Math. Soc. 45 (2008), 489-534.
- J.-G. Luque, J.-Y. Thibon, 2002