"Andrews-Garvan crank modular form"의 두 판 사이의 차이
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imported>Pythagoras0 (새 문서: ==introduction== $$ C(w;q)=\frac{(q)_{\infty}}{(wq;q)_{\infty}(w^{-1}q;q)_{\infty}} $$ ==related items== * Dyson's rank generating function * Quantum modular forms [[분...) |
imported>Pythagoras0 |
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| 3번째 줄: | 3번째 줄: | ||
C(w;q)=\frac{(q)_{\infty}}{(wq;q)_{\infty}(w^{-1}q;q)_{\infty}} | C(w;q)=\frac{(q)_{\infty}}{(wq;q)_{\infty}(w^{-1}q;q)_{\infty}} | ||
$$ | $$ | ||
| + | * specialization $C(-1;q)=b(q)$ where | ||
| + | $$b(q)=q^{1/24}\frac{\eta(\tau)}{\eta(2\tau)}\theta(-q)$$ | ||
| + | * see [[3rd order mock theta functions]] | ||
2013년 3월 18일 (월) 14:29 판
introduction
$$ C(w;q)=\frac{(q)_{\infty}}{(wq;q)_{\infty}(w^{-1}q;q)_{\infty}} $$
- specialization $C(-1;q)=b(q)$ where
$$b(q)=q^{1/24}\frac{\eta(\tau)}{\eta(2\tau)}\theta(-q)$$