"Q-analogue of summation formulas"의 두 판 사이의 차이
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* q-analogue of Whipple's theorem<br> | * q-analogue of Whipple's theorem<br> | ||
* Jackson's q-analogue of Dougall's theorem<br> | * Jackson's q-analogue of Dougall's theorem<br> | ||
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| 38번째 줄: | 12번째 줄: | ||
<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">books</h5> | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">books</h5> | ||
| − | * '''[GR2004]''' Gasper, George; Rahman, Mizan [http://books.google.com/books?id=31l4uC7lqGAC&dq=Gasper,+George;+Rahman,+Mizan+%282004%29,+Basic+hypergeometric+series | + | * '''[GR2004]''' Gasper, George; Rahman, Mizan [http://books.google.com/books?id=31l4uC7lqGAC&dq=Gasper,+George;+Rahman,+Mizan+%282004%29,+Basic+hypergeometric+series Basic hypergeometric series] 2004 |
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2011년 11월 12일 (토) 04:16 판
introduction
- 초기하 급수의 합공식
- q-Chu-Vandermonde
\(_2\phi_1(q^{-n},b;c;q,q)=\frac{(c/b;q)_n}{(c;q)_n}b^n\) - [GR2004] (1.5.1) Heine's q-analogue of Gauss' summation formula
\(_2\phi_1(a,b;c,q,c/ab)=\frac{(c/a;q)_{\infty}(c/b;q)_{\infty}}{(c;q)_{\infty}(c/(ab);q)_{\infty}}\) or
\(\sum_{n=0}^{\infty}\frac{(a,q)_{n}(b,q)_{n}}{(c ,q)_{n}(q ,q)_{n}}(\frac{c}{ab})^{n}=\frac{(c/a;q)_{\infty}(c/b;q)_{\infty}}{(c;q)_{\infty}(c/(ab);q)_{\infty}}\) - [GR2004] (1.7.2) q-analogue of Pfaff-Saalschutz's summation formula
\(_3\phi_2(a,b,q^{-n};c,abc^{-1}q^{1-n};q,q)=\frac{(c/a,c/b;q)_{n}}{(c,c/ab;q)_{n}}\) or
\(\sum_{n=0}^{\infty}\frac{(a,q)_{n}(b,q)_{n}(q^{-n},q)_{n}}{(c)_{n}(abc^{-1}q^{1-n} ,q)_{n}(q ,q)_{n}}q^{n}=\frac{(c/a,c/b;q)_{n}}{(c,c/ab;q)_{n}}\) - q-analogue of Whipple's theorem
- Jackson's q-analogue of Dougall's theorem
books
- [GR2004] Gasper, George; Rahman, Mizan Basic hypergeometric series 2004