On the meromorphic solutions of generalized q-difference equations
نویسندگان
چکیده
منابع مشابه
On meromorphic solutions of certain type of difference equations
We mainly discuss the existence of meromorphic (entire) solutions of certain type of non-linear difference equation of the form: $f(z)^m+P(z)f(z+c)^n=Q(z)$, which is a supplement of previous results in [K. Liu, L. Z. Yang and X. L. Liu, Existence of entire solutions of nonlinear difference equations, Czechoslovak Math. J. 61 (2011), no. 2, 565--576, and X. G. Qi...
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and Applied Analysis 3 where |q| > 1 and the index set J consists of m elements and the coefficients a i (z) (a n (z) = 1) and b J (z) are small functions of f. If f is of finite order, then |q| < n + m − 1. 2. Some Lemmas The following important result by Valiron andMohon’ko will be used frequently, one can find the proof in Laine’s book [16, page 29]. Lemma 9. Let f be a meromorphic function....
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It is shown that, if f is a meromorphic function of order zero and q ∈ C, then m „ r, f(qz) f(z) « = o(T (r, f)) (‡) for all r on a set of logarithmic density 1. The remainder of the paper consist of applications of identity (‡) to the study of value distribution of zero-order meromorphic functions, and, in particular, zero-order meromorphic solutions of q-difference equations. The results obta...
متن کاملon meromorphic solutions of certain type of difference equations
we mainly discuss the existence of meromorphic (entire) solutions of certain type of non-linear difference equation of the form: $f(z)^m+p(z)f(z+c)^n=q(z)$, which is a supplement of previous results in [k. liu, l. z. yang and x. l. liu, existence of entire solutions of nonlinear difference equations, czechoslovak math. j. 61 (2011), no. 2, 565--576, and x. g. qi...
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: ScienceAsia
سال: 2020
ISSN: 1513-1874
DOI: 10.2306/scienceasia1513-1874.2020.081