"Basic hypergeometric series"의 두 판 사이의 차이
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imported>Pythagoras0 잔글 (Pythagoras0 사용자가 3 q-series 문서를 Q-series 문서로 옮겼습니다.) |
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| − | + | == 하위페이지 == | |
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| + | * [[3 q-series]] | ||
| + | * [[Bailey pair and lemma]] | ||
| + | * [[Bailey lattice]] | ||
| + | * [[sources of Bailey pairs]] | ||
| + | * [[determinantal identities and Airy kernel]] | ||
| + | * [[elliptic hypergeometric series]] | ||
| + | * [[finitized q-series identity]] | ||
| + | * [[integer partitions]] | ||
| + | * [[q-analogue of summation formulas]] | ||
| + | * [[Slater list]] | ||
| + | * [[Slater 31]] | ||
| + | * [[Slater 32]] | ||
| + | * [[Slater 34]] | ||
| + | * [[Slater 36]] | ||
| + | * [[Slater 37]] | ||
| + | * [[Slater 47]] | ||
| + | * [[Slater 83]] | ||
| + | * [[Slater 86]] | ||
| + | * [[Slater 92]] | ||
| + | * [[Slater 98]] | ||
| + | * [[useful techniques in q-series]] | ||
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[[분류:math and physics]] | [[분류:math and physics]] | ||
2013년 12월 21일 (토) 02:47 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]
하위페이지
- 3 q-series
- Bailey pair and lemma
- Bailey lattice
- sources of Bailey pairs
- determinantal identities and Airy kernel
- elliptic hypergeometric series
- finitized q-series identity
- integer partitions
- q-analogue of summation formulas
- Slater list
- Slater 31
- Slater 32
- Slater 34
- Slater 36
- Slater 37
- Slater 47
- Slater 83
- Slater 86
- Slater 92
- Slater 98
- useful techniques in q-series