On Solutions of the q-Hypergeometric Equation with q N = 1
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We consider the q-hypergeometric equation with q^{N}=1 and $��, ��, ��\in {\Bbb Z}$. We solve this equation on the space of functions given by a power series multiplied by a power of the logarithmic function. We prove that the subspace of solutions is two-dimensional over the field of quasi-constants. We get a basis for this space explicitly. In terms of this basis, we represent the q-hypergeometric function of the Barnes type constructed by Nishizawa and Ueno. Then we see that this function has logarithmic singularity at the origin. This is a difference between the q-hypergeometric functions with 0
9 pages
\(q\)-hypergeometric equation, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Mathematics - Classical Analysis and ODEs, Mathematics - Quantum Algebra, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Quantum Algebra (math.QA), basic hypergeometric series, root of unity, Basic hypergeometric integrals and functions defined by them
\(q\)-hypergeometric equation, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Mathematics - Classical Analysis and ODEs, Mathematics - Quantum Algebra, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Quantum Algebra (math.QA), basic hypergeometric series, root of unity, Basic hypergeometric integrals and functions defined by them
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