"Basic hypergeometric series"의 두 판 사이의 차이
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Series[QPochhammer[q, q], {q, 0, 100}]<br> Series[\!\(<br> \*UnderoverscriptBox[\(\[Product]\), \(k = 1\), \(100\)]\((1 -<br> q^k)\)\), {q, 0, 100}]<br> f[q_] := \!\(<br> \*UnderoverscriptBox[\(\[Sum]\), \(k = 0\), \(100\)]\(PartitionsP[<br> k] q^k\)\)<br> Series[1/QPochhammer[q, q], {q, 0, 100}]<br> Series[f[q], {q, 0, 100}]<br> d[n_] := DivisorSigma[1, n]<br> g[q_] := \!\(<br> \*UnderoverscriptBox[\(\[Sum]\), \(k = 1\), \(100\)]\(d[k] q^k\)\)<br> Expand[f[q]*g[q]] | Series[QPochhammer[q, q], {q, 0, 100}]<br> Series[\!\(<br> \*UnderoverscriptBox[\(\[Product]\), \(k = 1\), \(100\)]\((1 -<br> q^k)\)\), {q, 0, 100}]<br> f[q_] := \!\(<br> \*UnderoverscriptBox[\(\[Sum]\), \(k = 0\), \(100\)]\(PartitionsP[<br> k] q^k\)\)<br> Series[1/QPochhammer[q, q], {q, 0, 100}]<br> Series[f[q], {q, 0, 100}]<br> d[n_] := DivisorSigma[1, n]<br> g[q_] := \!\(<br> \*UnderoverscriptBox[\(\[Sum]\), \(k = 1\), \(100\)]\(d[k] q^k\)\)<br> Expand[f[q]*g[q]] | ||
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| + | <h5>q-hypergeometric series</h5> | ||
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| + | <math>\sum_{n\geq 0}^{\infty}\frac{q^{n^2/2}}{(q)_n}\sim \exp(\frac{\pi^2}{12t}-\frac{t}{48})</math> | ||
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| 5번째 줄: | 17번째 줄: | ||
<h5>related items</h5> | <h5>related items</h5> | ||
| − | * [[ | + | * [[asymptotic analysis of basic hypergeometric series]] |
2010년 3월 21일 (일) 09:08 판
Series[QPochhammer[q, q], {q, 0, 100}]
Series[\!\(<br> \*UnderoverscriptBox[\(\[Product]\), \(k = 1\), \(100\)]\((1 -<br> q^k)\)\), {q, 0, 100}]
f[q_] := \!\(<br> \*UnderoverscriptBox[\(\[Sum]\), \(k = 0\), \(100\)]\(PartitionsP[<br> k] q^k\)\)
Series[1/QPochhammer[q, q], {q, 0, 100}]
Series[f[q], {q, 0, 100}]
d[n_] := DivisorSigma[1, n]
g[q_] := \!\(<br> \*UnderoverscriptBox[\(\[Sum]\), \(k = 1\), \(100\)]\(d[k] q^k\)\)
Expand[f[q]*g[q]]
q-hypergeometric series
\(\sum_{n\geq 0}^{\infty}\frac{q^{n^2/2}}{(q)_n}\sim \exp(\frac{\pi^2}{12t}-\frac{t}{48})\)