"Q-Chu-Vandermonde 항등식"의 두 판 사이의 차이

2011년 6월 18일 (토) 09:20 판

\( _2\phi_1(q^{-n},b;c;q,cq^n/b)=\frac{((cq^n;q)_\infty(c/b;q)_\infty)}{((c;q)_\infty(cq^n/b;q)_\infty)}=\frac{((c/b;q)_n)}{((c;q)_n)}\)

\(_2\phi_1(q^{-n},b;c;q,q)=\frac{((c/b;q)_n)}{((c;q)_n)}b^n\)

@@ 12번째 줄: / 12번째 줄: @@
-<math> _2\phi_1(q^{-n},b;c;q,cq^n/b)=((cq^n;q)_\infty(c/b;q)_\infty)/((c;q)_\infty(cq^n/b;q)_\infty)=((c/b;q)_n)/((c;q)_n), </math>
+<math> _2\phi_1(q^{-n},b;c;q,cq^n/b)=\frac{((cq^n;q)_\infty(c/b;q)_\infty)}{((c;q)_\infty(cq^n/b;q)_\infty)}=\frac{((c/b;q)_n)}{((c;q)_n)}</math>
-<math>_2\phi_1(q^{-n},b;c;q,q)=((c/b;q)_n)/((c;q)_n)b^n</math>
+<math>_2\phi_1(q^{-n},b;c;q,q)=\frac{((c/b;q)_n)}{((c;q)_n)}b^n</math>
@@ 75번째 줄: / 75번째 줄: @@
 <h5>사전 형태의 자료</h5>
-* http://ko.wikipedia.org/wiki/
+* http://en.wikipedia.org/wiki/Q-Vandermonde_identity
 * [http://en.wikipedia.org/wiki/Vandermonde%27s_identity http://en.wikipedia.org/wiki/Vandermonde's_identity]
 * http://en.wikipedia.org/wiki/
@@ 93번째 줄: / 93번째 줄: @@
 <h5>관련논문</h5>
+* [http://dx.doi.org/10.1016/0012-365X%2884%2990149-3 Some generalized Durfee square identities]<br>
+**  Ira M. Gessel, Discrete MathematicsVolume 49, Issue 1, March 1984, Pages 41-44<br>
+* [http://dx.doi.org/10.1016/S0096-3003%2896%2900054-9 Some combinatorial identities associated with the Vandermonde convolution]<br>
+**  H. W. Gould and H. M. Srivastava, 1997<br>
+* [http://www.jstor.org/stable/2306429 Some Generalizations of Vandermonde's Convolution]<br>
+**  H. W. Gould, The American Mathematical Monthly, Vol. 63, No. 2 (Feb., 1956), pp. 84-91<br>
 * http://www.jstor.org/action/doBasicSearch?Query=