"Basic hypergeometric series"의 두 판 사이의 차이
둘러보기로 가기
검색하러 가기
| 61번째 줄: | 61번째 줄: | ||
* [[3 q-series]]<br> | * [[3 q-series]]<br> | ||
** [[Bailey pair and lemma]]<br> | ** [[Bailey pair and lemma]]<br> | ||
| − | |||
*** [[Bailey lattice]]<br> | *** [[Bailey lattice]]<br> | ||
| − | *** [[sources of Bailey pairs | + | *** [[sources of Bailey pairs]]<br> |
** [[determinantal identities and Airy kernel]]<br> | ** [[determinantal identities and Airy kernel]]<br> | ||
** [[elliptic hypergeometric series]]<br> | ** [[elliptic hypergeometric series]]<br> | ||
| 70번째 줄: | 69번째 줄: | ||
** [[q-analogue of summation formulas]]<br> | ** [[q-analogue of summation formulas]]<br> | ||
** [[Slater list]]<br> | ** [[Slater list]]<br> | ||
| − | |||
| − | |||
| − | |||
| − | |||
*** [[Slater 31]]<br> | *** [[Slater 31]]<br> | ||
*** [[Slater 32]]<br> | *** [[Slater 32]]<br> | ||
2012년 8월 26일 (일) 07:16 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
KdV Hirota polynomials
- Series[1/QPochhammer[q, q^2] - 1/QPochhammer[q^2, q^4], {q, 0, 100}]
- KdV equation
- asymptotic analysis of basic hypergeometric series
- hypergeometric functions and representation theory
- [http://www.springerlink.com/content/j22163577187156l/ Common extension of bilateral series for Andrews’ q-Bailey and q-Gauss sums
Wenchang Chu and Chenying Wang]