منابع مشابه
q-Hypergeometric Series and Macdonald Functions
Abstract We derive a duality formula for two-row Macdonald functions by studying their relation with basic hypergeometric functions. We introduce two parameter vertex operators to construct a family of symmetric functions generalizing Hall-Littlewood functions. Their relation with Macdonald functions is governed by a very well-poised q-hypergeometric functions of type 4 0$, for which we obtain ...
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We present a systematic method for proving nonterminating basic hypergeometric identities. Assume that k is the summation index. By setting a parameter x to xqn, we may find a recurrence relation of the summation by using the q-Zeilberger algorithm. This method applies to almost all nonterminating basic hypergeometric summation formulas in the book of Gasper and Rahman. Furthermore, by comparin...
متن کاملMULTIPLICATIVE q-HYPERGEOMETRIC SERIES ARISING FROM REAL QUADRATIC FIELDS
Andrews, Dyson, and Hickerson showed that 2 q-hypergeometric series, going back to Ramanujan, are related to real quadratic fields, which explains interesting properties of their Fourier coefficients. There is also an interesting relation of such series to automorphic forms. Here we construct more such examples arising from interesting combinatorial statistics.
متن کاملQ-hypergeometric Solutions of Q-diierence Equations
We present algorithm qHyper for nding all solutions y(x) of a linear homogeneous q-diierence equation such that y(qx) = r(x)y(x) where r(x) is a rational function of x. Applications include construction of basic hypergeometric series solutions, and deenite q-hypergeometric summation in closed form.
متن کاملq-Hypergeometric solutions of q-difference equations
We present algorithm qHyper for finding all solutions y(x) of a linear homogeneous q-difference equation, such that y(qx) = r(x)y(x) where r(x) is a rational function of x. Applications include construction of basic hypergeometric series solutions, and definite q-hypergeometric summation in closed form. ∗The research described in this publication was made possible in part by Grant J12100 from t...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1995
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)00069-5