ON Q-SHIFT DIFFERENCE-DIFFERENTIAL POLYNOMIALS OF ENTIRE FUNCTIONS THAT SHARE ONE VALUE | ||
| Journal of Fractional Calculus and Applications | ||
| Article 9, Volume 15, Issue 1, January 2024, Pages 1-16 PDF (371.29 K) | ||
| Document Type: Regular research papers | ||
| DOI: 10.21608/jfca.2024.244952.1045 | ||
| Author | ||
| Abhijit Shaw* | ||
| Balagarh High School, Assistant Teacher, Department of Mathematics, Balagarh, Hooghly, WB, India-712136 | ||
| Abstract | ||
| In this article we addresses the product of q-shift difference of transcendental entire functions. We primarily examine the zero distribution of the q-shift difference-differential polynomials of transcendental entire functions while simultaneously preparing the answers to the uniqueness problem in the case where the q-shift difference-differential polynomials of transcendental entire functions share a constant value. The findings are based on I. Lahiri's \cite{9,10} introduction of the concept of weighted sharing. The theory of Picard's exceptional value play an effective role for finding of our the results. To discuss our results we create certain polynomial equation and analysed entire results of the article applying the theory of simple and multiple zeros of polynomial equation. We broadly elaborate our results with remark and corollary, and give an excellent example for proper justification of our results. Some open problems are generated from our results for future research. We extend and improve the results of R.S.Dyavanal and A.M.Hatticat \cite{4}, and generalized the result of P. Sahoo and G. Biswas \cite{21} in effective manner. | ||
| Keywords | ||
| Difference differential polynomials; Q-shift; Picard's exceptional values; Zero order; Uniqueness | ||
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