Growth and Approximation of Generalized Bi-Axially Symmetric Potentials
Received:December 12, 2014  Revised:May 27, 2015
Key Words: generalized bi-axially symmetric potentials   $q$-proximate order   Jacobi polynomials   generalized $q$-type   generalized lower $q$-type   approximation errors  
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Author NameAffiliation
Devendra KUMAR Department of Mathematics, Faculty of Science, Al-Baha University, P.O.Box-1988, Al-Baha-65431, Saudi Arabia, K. S. A 
Anindita BASU Department of Mathematics, Dr. Bhupendra Nath Dutta Smriti Mahavidyalaya, Burdwan, P.O Box-713407, West Bengal, India 
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      The paper deals with growth estimates and approximation (not necessarily entire) of solutions of certain elliptic partial differential equations. These solutions are called generalized bi-axially symmetric potentials (GBASP's). To obtain more refined measure of growth, we have defined $q$-proximate order and obtained the characterization of generalized $q$-type and generalized lower $q$-type with respect to $q$-proximate order of a GBASP in terms of approximation errors and ratio of these errors in sup norm.
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