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Laguerre-Type Exponentials, and the Relevant ๐ฟ-Circular and ๐ฟ-Hyperbolic Functions
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Giuseppe Dattoli
Published/Copyright:
March 10, 2010
Abstract
Some classes of entire functions which are eigenfunctions of generalizations of the Laguerre derivative operator are considered.
Since this property is an analog of the one characterizing the exponential function, we refer to such functions as Laguerre-type exponentials, or shortly ๐ฟ-exponentials. The definition of ๐ฟ-circular and ๐ฟ-hyperbolic functions easily follows.
Applications in the framework of generalized evolution problems are also mentioned.
Key words and phrases:: Laguerre derivative; Tricomi functions; Laguerre-type exponential functions; ๐ฟ-circular and ๐ฟ-hyperbolic functions
Received: 2002-12-25
Published Online: 2010-03-10
Published in Print: 2003-September
ยฉ Heldermann Verlag
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Keywords for this article
Laguerre derivative;
Tricomi functions;
Laguerre-type exponential functions;
๐ฟ-circular and ๐ฟ-hyperbolic functions
Articles in the same Issue
- On Fourier Series in Eigenfunctions of Elliptic Boundary Value Problems
- On the Mathematical Basis of the Linear Sampling Method
- Solvability and Asymptotics of Solutions of Crack-Type Boundary-Contact Problems of the Couple-Stress Elasticity
- Integral Representations for the Solution of Dynamic Bending of a Plate with Displacement-Traction Boundary Data
- Laguerre-Type Exponentials, and the Relevant ๐ฟ-Circular and ๐ฟ-Hyperbolic Functions
- About Asymptotic and Oscillation Properties of the Dirichlet Problem for Delay Partial Differential Equations
- The Superstability of the Generalized D'alembert Functional Equation
- First Order Partial Functional Differential Equations with Unbounded Delay
- The Dirichlet Problem for Harmonic Functions with Boundary Values from Zygmund Classes
- On the Asymptotics of Solutions of Elliptic Equations in a Neighborhood of a Crack with Nonsmooth Front
- A Factorization Method for an Inverse Neumann Problem for Harmonic Vector Fields
- A Bound for Reflections Across Jordan Curves
- A Direct Method for Boundary Integral Equations on a Contour with a Peak
- On Two-Point Boundary Value Problems for Two-Dimensional Differential Systems with Singularities
