New multiple 6ψ6 summation formulas and related conjectures

Spiridonov, Vyacheslav P. and Warnaar, S. Ole (2011) New multiple 6ψ6 summation formulas and related conjectures. The Ramanujan Journal, 25 3: 319-342. doi:10.1007/s11139-011-9310-5

Author Spiridonov, Vyacheslav P.
Warnaar, S. Ole
Title New multiple 6ψ6 summation formulas and related conjectures
Journal name The Ramanujan Journal   Check publisher's open access policy
ISSN 1382-4090
Publication date 2011-08
Sub-type Article (original research)
DOI 10.1007/s11139-011-9310-5
Volume 25
Issue 3
Start page 319
End page 342
Total pages 24
Place of publication New York, United States
Publisher Springer New York
Collection year 2012
Language eng
Formatted abstract
Three new summation formulas for 6ψ6 bilateral basic hypergeometric series
attached to root systems are presented. Remarkably, two of these formulae, labelled
by the A2n−1 and A2n root systems, can be reduced to multiple 6φ5 sums
generalising the well-known van Diejen sum. This latter sum serves as the weightfunction normalisation for the BCn q-Racah polynomials of van Diejen and Stokman. Two 8φ7-level extensions of the multiple 6φ5 sums, as well as their elliptic analogues,
are conjectured. This opens up the prospect of constructing novel A-type extensions
of the Koornwinder–Macdonald theory.
Keyword Basic hypergeometric series
Elliptic hypergeometric series
Root systems
Orthogonal polynomials
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Dedicated to George Andrews on the occasion of his 70th birthday

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2012 Collection
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Citation counts: TR Web of Science Citation Count  Cited 1 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 1 times in Scopus Article | Citations
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Created: Fri, 14 Oct 2011, 14:37:50 EST by Professor Ole Warnaar on behalf of Mathematics