"Basic hypergeometric series"의 두 판 사이의 차이
둘러보기로 가기
검색하러 가기
37번째 줄: | 37번째 줄: | ||
http://www.springerlink.com/content/j22163577187156l/ | http://www.springerlink.com/content/j22163577187156l/ | ||
+ | |||
+ | |||
+ | |||
+ | |||
+ | |||
+ | ==== 하위페이지 ==== | ||
+ | |||
+ | * [[3 q-series|q-series]]<br> | ||
+ | ** [[asymptotic analysis of basic hypergeometric series]]<br> | ||
+ | ** [[Bailey pair and lemma|Bailey's lemma]]<br> | ||
+ | ** [[Hardy-Ramanujan tauberian theorem]]<br> | ||
+ | ** [[integer partitions]]<br> | ||
+ | ** [[minimal models(mathematica)]]<br> | ||
+ | ** [[Slater list|Slater's list]]<br> | ||
+ | *** [[5960113|Slater 09]]<br> | ||
+ | *** [[5974537|Slater 18]]<br> | ||
+ | *** [[Slater 92]]<br> |
2010년 6월 23일 (수) 18:34 판
theory
- 오일러의 오각수정리(pentagonal number theorem)
\((1-x)(1-x^2)(1-x^3) \cdots = 1 - x - x^2 + x^5 + x^7 - x^{12} - x^{15} + x^{22} + x^{26} + \cdots\) - 오일러공식
\(\prod_{n=0}^{\infty}(1+zq^n)=\sum_{n\geq 0}\frac{q^{n(n-1)/2}}{(1-q)(1-q^2)\cdots(1-q^n)} z^n\)
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
http://www.springerlink.com/content/j22163577187156l/