"Basic hypergeometric series"의 두 판 사이의 차이
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# f[q_] := QHypergeometricPFQ[{}, {}, q, -q^(1/2)]<br> g[q_] := Exp[-(Pi^2/(12 Log[q])) + Log[q]/48]<br> Table[N[f[1 - 1/10^(i)]/g[1 - 1/10^(i)], 50], {i, 1, 5}] // TableForm | # f[q_] := QHypergeometricPFQ[{}, {}, q, -q^(1/2)]<br> g[q_] := Exp[-(Pi^2/(12 Log[q])) + Log[q]/48]<br> Table[N[f[1 - 1/10^(i)]/g[1 - 1/10^(i)], 50], {i, 1, 5}] // TableForm | ||
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2011년 4월 23일 (토) 16:42 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
- 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]