Euler transformation formula for multiple basic hypergeometric series of type A and some applications
Euler transformation formula for multiple basic hypergeometric series of type A and some applications
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A型多重基本超几何级数的欧拉变换公式及一些应用
DOI：
10.1016/j.aim.2003.08.012
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发表时间：
2004
影响因子：
1.7
通讯作者：
Yasushi Kajihara
中科院分区：
文献类型：
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作者：
Yasushi Kajihara
导出了基本超几何级数2φ1的欧拉变换公式的一个多重推广。利用多主专门化方法，从麦克唐纳多项式再现核的对称性出发，得到了麦克唐纳多项式再现核的对称性。作为应用，给出了U（n+1）中由于S.C. Milne的基本超几何级数的Pfaff-Saalschutz求和公式和Gauss求和公式的初等证明。并给出了非常匀称的10φ9、8φ7系、平衡的4φ3、3φ2系的其他一些多重变换和求和公式。
A multiple generalization of the Euler transformation formula for basic hypergeometric series2φ1is derived. It is obtained from the symmetry of the reproducing kernel for Macdonald polynomials by a method of multiple principal specialization. As applications, elementary proofs of the Pfaff–Saalschutz summation formula and the Gauss summation formula for basic hypergeometric series in U(n+1) due to S.C. Milne are given. Some other multiple transformation and summation formulas for very-well-poised10φ9and8φ7series, balanced4φ3series and3φ2series are also given.