Bohr’s Phenomenon for the Solution of Second-Order Differential Equations

Saiful R. Mondal ()
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Saiful R. Mondal: Department of Mathematics and Statistics, Collage of Science, King Faisal University, Al-Hasa 31982, Saudi Arabia

Mathematics, 2023, vol. 12, issue 1, 1-17

Abstract: The aim of this work is to establish a connection between Bohr’s radius and the analytic and normalized solutions of two differential second-order differential equations, namely y ″ ( z ) + a ( z ) y ′ ( z ) + b ( z ) y ( z ) = 0 and z 2 y ″ ( z ) + a ( z ) y ′ ( z ) + b ( z ) y ( z ) = d ( z ) . Using differential subordination, we find the upper bound of the Bohr and Rogosinski radii of the normalized solution F ( z ) of the above differential equations. We construct several examples by judicious choice of a ( z ) , b ( z ) and d ( z ) . The examples include several special functions like Airy functions, classical and generalized Bessel functions, error functions, confluent hypergeometric functions and associate Laguerre polynomials.

Keywords: Bohr’s phenomenon; second-order differential equation; subordination; Bessel functions; Airy functions; error function; confluent hypergeometric functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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