A First Order q-Difference System for the BC 1 -Type Jackson Integral and Its Applications
Copyright policy )A First Order q-Difference System for the BC 1 -Type Jackson Integral and Its Applications
We present an explicit expression for the $q$-difference system, which the $BC_1$-type Jackson integral ($q$-series) satisfies, as first order simultaneous $q$-difference equations with a concrete basis. As an application, we give a simple proof for the hypergeometric summation formula introduced by Gustafson and the product formula of the $q$-integral introduced by Nassrallah-Rahman and Gustafson.
- Aoyama Gakuin University Japan
q-difference equations, Jackson integral of type BC_1, Difference equations, scaling (\(q\)-differences), Jackson integral of type \(BC_{1}\), \(q\)-difference equations, Gustafson's C_n-type sum, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Mathematics - Classical Analysis and ODEs, QA1-939, Nassrallah-Rahman integral, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Gustafson's \(C_n\)-type sum, Mathematics, Basic hypergeometric functions associated with root systems
q-difference equations, Jackson integral of type BC_1, Difference equations, scaling (\(q\)-differences), Jackson integral of type \(BC_{1}\), \(q\)-difference equations, Gustafson's C_n-type sum, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Mathematics - Classical Analysis and ODEs, QA1-939, Nassrallah-Rahman integral, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Gustafson's \(C_n\)-type sum, Mathematics, Basic hypergeometric functions associated with root systems
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