"르벡 항등식"의 두 판 사이의 차이

2020년 11월 16일 (월) 06:33 판

[Alladi&Gordon1993] 278&279p\[f(a,c)=\sum_{k\geq 0}\frac{a^{k}q^{k(k-1)/2}(-cq)_{k}}{(q)_{k}}\]

a=q, c=z일 때, 르벡 항등식 (Lebesgue's identity) 을 얻는다\[f(q,z)=\sum_{k\geq 0}\frac{q^{k}q^{k(k-1)/2}(-zq)_{k}}{(q)_{k}}=\sum_{k\geq 0}\frac{q^{k(k+1)/2}(-zq)_{k}}{(q)_{k}}=(-zq^2;q^2)_{\infty}(-q)_{\infty}=\prod_{m=1}^{\infty} (1+zq^{2m})(1+q^{m})\]

[Alladi&Gordon1993]Partition identities and a continued fraction of Ramanujan ,Krishnaswami Alladi and Basil Gordon, 1993

@@ 1번째 줄: / 1번째 줄: @@
 ==개요==
-* '''[Alladi&Gordon1993] 278&279p''':<math>f(a,c)=\sum_{k\geq 0}\frac{a^{k}q^{k(k-1)/2}(-cq)_{k}}{(q)_{k}}</math><br>
+* '''[Alladi&Gordon1993] 278&279p''':<math>f(a,c)=\sum_{k\geq 0}\frac{a^{k}q^{k(k-1)/2}(-cq)_{k}}{(q)_{k}}</math>
-*  a=q, c=z일 때, 르벡 항등식 (Lebesgue's identity) 을 얻는다:<math>f(q,z)=\sum_{k\geq 0}\frac{q^{k}q^{k(k-1)/2}(-zq)_{k}}{(q)_{k}}=\sum_{k\geq 0}\frac{q^{k(k+1)/2}(-zq)_{k}}{(q)_{k}}=(-zq^2;q^2)_{\infty}(-q)_{\infty}=\prod_{m=1}^{\infty} (1+zq^{2m})(1+q^{m})</math><br>
+*  a=q, c=z일 때, 르벡 항등식 (Lebesgue's identity) 을 얻는다:<math>f(q,z)=\sum_{k\geq 0}\frac{q^{k}q^{k(k-1)/2}(-zq)_{k}}{(q)_{k}}=\sum_{k\geq 0}\frac{q^{k(k+1)/2}(-zq)_{k}}{(q)_{k}}=(-zq^2;q^2)_{\infty}(-q)_{\infty}=\prod_{m=1}^{\infty} (1+zq^{2m})(1+q^{m})</math>