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Generalized growth and weighted polynomial approximation of entire function solutions of certain elliptic partial differential equation

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Abstract

The paper deals with the study of generalized growth and \(L^\delta -\)approximation \((1\le \delta \le \infty )\) of entire function solutions of certain elliptic partial differential equation in the sense of Sheremeta (Am Math Soc Transl 88:291–301). Moreover, the characterization of generalized order and generalized type of these solutions which are known as generalized axisymmetric potentials (GASP’s), in terms of decay of approximation error \(E_n(H,R_0)\) and weighted approximation errors \(E^i_{n,\delta }(H,R_0),i=1,2\) have been obtained.

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Acknowledgements

The authors are very much thankful to learned reviewer for giving fruitful comments to improve the paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Al-Baha University, P.O.-Box-1988, Alaqiq, Al-Baha, 65431, Saudi Arabia

    Devendra Kumar

  2. Department of Mathematics, Seth Anandram Jaipuria College, 10, Raja Naba Krishna Street, Kolkata, 700005, India

    Anindita Basu

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  1. Devendra Kumar
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  2. Anindita Basu
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Correspondence to Devendra Kumar.

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Kumar, D., Basu, A. Generalized growth and weighted polynomial approximation of entire function solutions of certain elliptic partial differential equation. J Anal (2023). https://doi.org/10.1007/s41478-023-00671-7

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