Abstract
We prove a general quadratic formula for basic hypergeometric series, from which simple proofs of several recent determinant and Pfaffian formulas are obtained. A special case of the quadratic formula is actually related to a Gram determinant formula for Askey-Wilson polynomials. We also show how to derive a recent double-sum formula for the moments of Askey- Wilson polynomials from Newton’s interpolation formula.
| Original language | English |
|---|---|
| Pages (from-to) | 2003-2015 |
| Number of pages | 13 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 143 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 2015 |
| Externally published | Yes |
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Keywords
- Askey-Wilson polynomials
- Desnanot–Jacobi adjoint matrix theorem
- Gram determinants
- Moments of Askey-Wilson polynomials
- Pfaffians
- Quadratic formula of basic hypergeometric series
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
Cite this
A quadratic formula for basic hypergeometric series related to Askey-Wilson polynomials. / Guo, Victor J W; Ishikawa, Masao; Tagawa, Hiroyuki; Zeng, Jiang.
In: Proceedings of the American Mathematical Society, Vol. 143, No. 5, 2015, p. 2003-2015.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A quadratic formula for basic hypergeometric series related to Askey-Wilson polynomials
AU - Guo, Victor J W
AU - Ishikawa, Masao
AU - Tagawa, Hiroyuki
AU - Zeng, Jiang
PY - 2015
Y1 - 2015
N2 - We prove a general quadratic formula for basic hypergeometric series, from which simple proofs of several recent determinant and Pfaffian formulas are obtained. A special case of the quadratic formula is actually related to a Gram determinant formula for Askey-Wilson polynomials. We also show how to derive a recent double-sum formula for the moments of Askey- Wilson polynomials from Newton’s interpolation formula.
AB - We prove a general quadratic formula for basic hypergeometric series, from which simple proofs of several recent determinant and Pfaffian formulas are obtained. A special case of the quadratic formula is actually related to a Gram determinant formula for Askey-Wilson polynomials. We also show how to derive a recent double-sum formula for the moments of Askey- Wilson polynomials from Newton’s interpolation formula.
KW - Askey-Wilson polynomials
KW - Desnanot–Jacobi adjoint matrix theorem
KW - Gram determinants
KW - Moments of Askey-Wilson polynomials
KW - Pfaffians
KW - Quadratic formula of basic hypergeometric series
UR - http://www.scopus.com/inward/record.url?scp=84923239760&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84923239760&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-2015-12099-0
DO - 10.1090/S0002-9939-2015-12099-0
M3 - Article
AN - SCOPUS:84923239760
VL - 143
SP - 2003
EP - 2015
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 5
ER -