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During the last decade, several papers have focused on linear q-difference equations of the form n X j=0 aj (z)f(qjz) = an+1(z) with entire or meromorphic coefficients. A tool for studying these equations is a q-difference analogue of the lemma on the logarithmic derivative, valid for meromorphic functions of finite logarithmic order log. It is shown, under certain assumptions, that log(f) = max{ log(aj )} + 1.
Moreover, it is illustrated that a q-Casorati determinant plays a similar role in the theory of linear q-difference equations as a Wronskian determinant in the theory of linear differential equations. As a consequence of the main results, it follows that the q-gamma function and the q-exponential functions all have logarithmic order two.
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참고문헌 (21)
참고문헌 신청
A. A. Goldberg / 2008 / Translations of Mathematical Monographs, 236 / American Mathematical Society
B. -Q. Chen / 2010 / Properties on solutions of some q-difference equa-tions / Acta Math. Sin. (Engl. Ser.) 26 (10) : 1877 ~ 1886
BaoQin Chen / 2011 / Meromorphic solutions of some q-difference equations / 대한수학회보 48 (6) : 1303 ~ 1314
C. Berg / 2007 / Difference equations, special functions and orthogonal polynomials / World Sci. Publ : 51 ~ 79
D. C. Barnett / 2007 / Nevanlinna theory for the q-difference operator and meromorphic solutions of q-difference equations / Proc. Roy. Soc. Edinburgh Sect. A 137 (3) : 457 ~
B. -Q. Chen / 2010 / Properties on solutions of some q-difference equa-tions / Acta Math. Sin. (Engl. Ser.) 26 (10) : 1877 ~ 1886
BaoQin Chen / 2011 / Meromorphic solutions of some q-difference equations / 대한수학회보 48 (6) : 1303 ~ 1314
C. Berg / 2007 / Difference equations, special functions and orthogonal polynomials / World Sci. Publ : 51 ~ 79
D. C. Barnett / 2007 / Nevanlinna theory for the q-difference operator and meromorphic solutions of q-difference equations / Proc. Roy. Soc. Edinburgh Sect. A 137 (3) : 457 ~
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