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The uniqueness problems on entire functions sharing at least two values with their derivatives or linear differential polynomials have been studied and many results on this topic have been obtained. In this paper, we study an entire function $f(z)$ that shares a nonzero polynomial $a(z)$ with $f^{(1)}(z)$, together with its linear differential polynomials of the form: $L=L(f)=a_{1}(z)f^{(1)}(z)+a_{2}(z)f^{(2)}(z)+\cdots+a_{n}(z)f^{(n)}(z)$, where the coefficients $a_{k}(z) (k=1,2,\ldots,n)$ are rational functions and $a_{n}(z)\not\equiv 0$.
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참고문헌 (11)
참고문헌 신청
J. Chang / 2004 / Entire functions that share a small function with their derivatives / Complex Var. Theory Appl. 49(12):871~895
W. K. Hayman / 1964 / Meromorphic Functions, Oxford Math. Monogr. / Clarendon Press
G. Jank / 1986 / Meromorphe Funktionen, die mit ihrer ersten und zweiten Ableitung einen endlichen Wert teilen / Complex Variables Theory Appl. 6(1):51~71
I. Lahiri / 2011 / Entire functions sharing values with their derivatives / Analysis (Munich) 31(1):47~59
P. Li / 1999 / Entire functions that share one value with their linear differential polynomials / Kodai Math. J. 22(3):446~457
W. K. Hayman / 1964 / Meromorphic Functions, Oxford Math. Monogr. / Clarendon Press
G. Jank / 1986 / Meromorphe Funktionen, die mit ihrer ersten und zweiten Ableitung einen endlichen Wert teilen / Complex Variables Theory Appl. 6(1):51~71
I. Lahiri / 2011 / Entire functions sharing values with their derivatives / Analysis (Munich) 31(1):47~59
P. Li / 1999 / Entire functions that share one value with their linear differential polynomials / Kodai Math. J. 22(3):446~457
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