Basic hypergeometric series
http://bomber0.myid.net/ (토론)님의 2010년 3월 21일 (일) 09:34 판
theory
q-Pochhammer
- partition generating function
- Series[1/QPochhammer[q, q], {q, 0, 100}]
- Dedekind eta
- Series[QPochhammer[q, q], {q, 0, 100}]
q-hypergeometric series
\(\sum_{n\geq 0}^{\infty}\frac{q^{n^2/2}}{(q)_n}\sim \exp(\frac{\pi^2}{12t}-\frac{t}{48})\)
- f[q_] := QHypergeometricPFQ[{}, {}, q, -q^(1/2)]
g[q_] := Exp[-(Pi^2/(12 Log[q])) + Log[q]/48]
Table[N[f[1 - 1/10^(i)]/g[1 - 1/10^(i)], 50], {i, 1, 5}] // TableForm