On the Generating Functions and Special Functions Associated with Superoscillations
Copyright policy )On the Generating Functions and Special Functions Associated with Superoscillations
The aim of this paper is to study generating functions for the coefficients of the classical superoscillatory function associated with weak measurements. We also establish some new relations between the superoscillatory coefficients and many well-known families of special polynomials, numbers, and functions such as Bernstein basis functions, the Hermite polynomials, the Stirling numbers of second kind, and also the confluent hypergeometric functions. Moreover, by using generating functions, we are able to develop a recurrence relation and a derivative formula for the superoscillatory coefficients.
18 pages
- University of Erfurt Germany
- Polytechnic University of Milan Italy
- Akdeniz University Turkey
Hermite polynomials, 33C15, 32A15, 47B38, Operations and polynomials in algebraic structures, primal algebras, Generating functions for superoscillations, Bernstein basis functions, Perturbation theories for operators and differential equations in quantum theory, FOS: Physical sciences, Quantum measurement theory, state operations, state preparations, Mathematical Physics (math-ph), generating functions for superoscillations, Stirling numbers, superoscillating functions, Mathematics - Classical Analysis and ODEs, Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\), Classical Analysis and ODEs (math.CA), FOS: Mathematics, Resonance in context of PDEs, Mathematics - Combinatorics, Vector-valued set functions, measures and integrals, Combinatorics (math.CO), Superoscillating functions, Mathematical Physics
Hermite polynomials, 33C15, 32A15, 47B38, Operations and polynomials in algebraic structures, primal algebras, Generating functions for superoscillations, Bernstein basis functions, Perturbation theories for operators and differential equations in quantum theory, FOS: Physical sciences, Quantum measurement theory, state operations, state preparations, Mathematical Physics (math-ph), generating functions for superoscillations, Stirling numbers, superoscillating functions, Mathematics - Classical Analysis and ODEs, Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\), Classical Analysis and ODEs (math.CA), FOS: Mathematics, Resonance in context of PDEs, Mathematics - Combinatorics, Vector-valued set functions, measures and integrals, Combinatorics (math.CO), Superoscillating functions, Mathematical Physics
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