"Basic hypergeometric series"의 두 판 사이의 차이

2010년 9월 25일 (토) 23:51 판

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
\(\prod_{n=0}^{\infty}(1+zq^n)=\sum_{n\geq 0}\frac{q^{n(n-1)/2}}{(1-q)(1-q^2)\cdots(1-q^n)} z^n\)

\(\sum_{n\geq 0}^{\infty}\frac{q^{n^2/2}}{(q)_n}\sim \exp(\frac{\pi^2}{12t}-\frac{t}{48})\)

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

@@ 37번째 줄: / 37번째 줄: @@
 http://www.springerlink.com/content/j22163577187156l/
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 ==== 하위페이지 ====
-* [[3 q-series|q-series]]<br>
+* [[3 q-series]]<br>
-** [[asymptotic analysis of basic hypergeometric series]]<br>
+** [[Bailey pair and lemma]]<br>
-** [[Bailey pair and lemma|Bailey's lemma]]<br>
+*** [[6080259|Bailey chain]]<br>
-** [[Hardy-Ramanujan tauberian theorem]]<br>
+*** [[Bailey lattice]]<br>
+*** [[sources of Bailey pairs|Bailey pairs from CFT]]<br>
+** [[finitized q-series identity]]<br>
 ** [[integer partitions]]<br>
-** [[minimal models(mathematica)]]<br>
+** [[q-analogue of summation formulas]]<br>
-** [[q-analogue of summation formulas|q-Gauss summation]]<br>
+** [[Slater list]]<br>
-** [[Slater list|Slater's list]]<br>
+*** [[6078351|Slater 02]]<br>
-*** [[5960113|Slater 09]]<br>
+*** [[5960113|Slater 08]]<br>
+*** [[5984287|Slater 14]]<br>
 *** [[5974537|Slater 18]]<br>
+*** [[Slater 34]]<br>
+*** [[Slater 36]]<br>
+*** [[Slater 37]]<br>
+*** [[Slater 47]]<br>
+*** [[Slater 83]]<br>
+*** [[Slater 86]]<br>
 *** [[Slater 92]]<br>
+*** [[Slater 98]]<br>
+** [[useful techniques in q-series]]<br>
+** [[6162505|Vandermonde convolution]]<br>