Uniqueness of Entire Functions Sharing Polynomials with Their Derivatives
We use the theory of normal families to prove the following. Let Q1(z)=a1zp+a1,p−1zp−1+⋯+a1,0 and Q2(z)=a2zp+a2,p−1zp−1+⋯+a2,0 be two polynomials such that degQ1=degQ2=p (where p is a nonnegative integer) and a1,a2(a2≠0) are two distinct complex numbers. Let f(z) be a transcendental entire functio...
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Wiley
2009-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2009/847690 |
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| author | Jianming Qi Feng Lü Ang Chen |
| author_facet | Jianming Qi Feng Lü Ang Chen |
| author_sort | Jianming Qi |
| collection | DOAJ |
| description | We use the theory of normal families to prove the following. Let Q1(z)=a1zp+a1,p−1zp−1+⋯+a1,0 and Q2(z)=a2zp+a2,p−1zp−1+⋯+a2,0 be two polynomials such that degQ1=degQ2=p (where p is a nonnegative integer) and a1,a2(a2≠0) are two distinct complex numbers. Let f(z) be a transcendental entire function. If f(z) and f′(z) share the polynomial Q1(z) CM and if f(z)=Q2(z) whenever f′(z)=Q2(z), then f≡f′. This result improves a result due to Li and Yi. |
| format | Article |
| id | doaj-art-e4688518b54f4b638308f7c5cf7b072b |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e4688518b54f4b638308f7c5cf7b072b2025-08-20T02:21:34ZengWileyAbstract and Applied Analysis1085-33751687-04092009-01-01200910.1155/2009/847690847690Uniqueness of Entire Functions Sharing Polynomials with Their DerivativesJianming Qi0Feng Lü1Ang Chen2School of Mathematics and System Sciences, Shandong University, Jinan, Shandong 250100, ChinaDepartment of Mathematics, China University of Petroleum, Dongying, Shandong 257061, ChinaSchool of Mathematics and System Sciences, Shandong University, Jinan, Shandong 250100, ChinaWe use the theory of normal families to prove the following. Let Q1(z)=a1zp+a1,p−1zp−1+⋯+a1,0 and Q2(z)=a2zp+a2,p−1zp−1+⋯+a2,0 be two polynomials such that degQ1=degQ2=p (where p is a nonnegative integer) and a1,a2(a2≠0) are two distinct complex numbers. Let f(z) be a transcendental entire function. If f(z) and f′(z) share the polynomial Q1(z) CM and if f(z)=Q2(z) whenever f′(z)=Q2(z), then f≡f′. This result improves a result due to Li and Yi.http://dx.doi.org/10.1155/2009/847690 |
| spellingShingle | Jianming Qi Feng Lü Ang Chen Uniqueness of Entire Functions Sharing Polynomials with Their Derivatives Abstract and Applied Analysis |
| title | Uniqueness of Entire Functions Sharing Polynomials with Their Derivatives |
| title_full | Uniqueness of Entire Functions Sharing Polynomials with Their Derivatives |
| title_fullStr | Uniqueness of Entire Functions Sharing Polynomials with Their Derivatives |
| title_full_unstemmed | Uniqueness of Entire Functions Sharing Polynomials with Their Derivatives |
| title_short | Uniqueness of Entire Functions Sharing Polynomials with Their Derivatives |
| title_sort | uniqueness of entire functions sharing polynomials with their derivatives |
| url | http://dx.doi.org/10.1155/2009/847690 |
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