##### This material has been published in
"*q*-Series with
Applications to Combinatorics, Number Theory, and Physics,"
Urbana-Champaign, Oct. 26-28, 2000, B. C. Berndt, K. Ono, eds.,
Contemporary Math., vol. 291, Amer. Math. Soc., Providence,
R.I., 2001, pp. 153-161,
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## Christian Krattenthaler

# Proof of a summation formula for an *Ã*_{n}
basic hypergeometric series conjectured by Warnaar

### (9 pages)

**Abstract.**
A proof of an unusual summation formula for a basic hypergeometric
series associated to the affine root system *Ã*_{n}
that was conjectured by Warnaar is given. It makes use of
Milne's *A*_{n} extension of Watson's transformation, Ramanujan's
_{1}*psi*_{1}-summation, and a determinant evaluation of the author.
In addition, a transformation formula between basic hypergeometric
series associated to the affine root systems *Ã*_{n}
respectively *Ã*_{n}, which generalizes at the same time the above
summation formula and an identity due to Gessel and
the author, is proposed as a conjecture.

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