Effect on the human liver cell proliferation after caveolin-1 gene knock-down

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• 作者：Gang Ren ; Ying Liu ; Xiao Min Wang ; Wei Zou
• 关键词：Operator identity ; Multiple q-series identity ; Bivariate Rogers– ; Szegö ; polynomial ; Mehler's formula ; Rogers's formula ; Milne's fundamental theorem for none ; color ; black" href="/science?_ob=Ma
• 刊名：Cell Biology International
• 出版年：2008
• 期刊代码：164_10656995
• 类别：bio
• 出版时间：March 2008
• 卷：32
• 期：3
• 页码：S45
• 文件大小：43 K

摘要

In this paper, we first give several operator identities involving the bivariate Rogers–Szegö polynomials. By applying the technique of parameter augmentation to the multiple q-binomial theorems given by Milne [S.C. Milne, Balanced d60fc533d38"> summation theorems for U(n) basic hypergeometric series, Adv. Math. 131 (1997) 93–187], we obtain several new multiple q-series identities involving the bivariate Rogers–Szegö polynomials. These include multiple extensions of Mehler's formula and Rogers's formula. Our 20d0d21b0a2cd2" title="Click to view the MathML source" alt="Click to view the MathML source">U(n+1) generalizations are quite natural as they are also a direct and immediate consequence of their (often classical) known one-variable cases and Milne's fundamental theorem for A_n or U(n+1) basic hypergeometric series in Theorem 1.49 of [S.C. Milne, An elementary proof of the Macdonald identities for , Adv. Math. 57 (1985) 34–70], as rewritten in Lemma 7.3 on p. 163 of [S.C. Milne, Balanced summation theorems for U(n) basic hypergeometric series, Adv. Math. 131 (1997) 93–187] or Corollary 4.4 on pp. 768–769 of [S.C. Milne, M. Schlosser, A new A_n extension of Ramanujan's summation with applications to multilateral A_n series, Rocky Mountain J. Math. 32 (2002) 759–792].