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Meromorphic functions of finite \(\varphi \)-order and linear Askey-Wilson divided difference equations. (English) Zbl 1484.39019

Summary: The growth of meromorphic solutions of linear difference equations containing Askey-Wilson divided difference operators is estimated. The \(\varphi \)-order is used as a general growth indicator, which covers the growth spectrum between the logarithmic order \(\rho_{\text{log}}(f)\) and the classical order \(\rho (f)\) of a meromorphic function \(f\).

MSC:

39A45 Difference equations in the complex domain
39A13 Difference equations, scaling (\(q\)-differences)
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
33E30 Other functions coming from differential, difference and integral equations
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References:

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