A generalization of the Sears-Slater transformation and elliptic Lagrange interpolation of type BC_n

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• 作者：Masahiko Ito^a ; ^{mito@cck.dendai.ac.jp" class="auth_mail" title="E-mail the corresponding author} ; Masatoshi Noumi^b ; ^{noumi@math.kobe-u.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 33D67 ; secondary ; 39A13
• 刊名：Advances in Mathematics
• 出版年：2016
• 出版时间：20 August 2016
• 年：2016
• 卷：299
• 期：Complete
• 页码：361-380
• 全文大小：415 K

文摘

The connection formula for the Jackson integral of type class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0001870816306363&_mathId=si1.gif&_user=111111111&_pii=S0001870816306363&_rdoc=1&_issn=00018708&md5=98d29e2a94be592bdc7cc4c4723ec074" title="Click to view the MathML source">BC_nclass="mathContainer hidden">class="mathCode">$B{C}_n$ is obtained in the form of a Sears–Slater type expansion of a bilateral multiple basic hypergeometric series as a linear combination of several specific bilateral multiple series. The coefficients of this expansion are expressed by certain elliptic Lagrange interpolation functions. Analyzing basic properties of the elliptic Lagrange interpolation functions, an explicit determinant formula is provided for a fundamental solution matrix of the associated system of q-difference equations.