1,096 research outputs found
Bunching coefficients in Echo-Enabled Harmonic Generation
Coulombian diffusion determines a dilution of bunching coefficients in Free
Electron Laser seeded devices. From the mathematical point of view the effect
can be modeled through a heat type equation, which can be merged with the
ordinary Liouville equation, ruling the evolution of the longitudinal phase
space beam distribution. We will show that the use of analytical tools like the
Generalized Bessel Functions and algebraic techniques for the solution of
evolution problems may provide a useful method of analysis and shine further
light on the physical aspects of the underlying mechanisms
The Ramanujan master theorem and its implications for special functions
We study a number of possible extensions of the Ramanujan master theorem,
which is formulated here by using methods of Umbral nature. We discuss the
implications of the procedure for the theory of special functions, like the
derivation of formulae concerning the integrals of products of families of
Bessel functions and the successive derivatives of Bessel type functions. We
stress also that the procedure we propose allows a unified treatment of many
problems appearing in applications, which can formally be reduced to the
evaluation of exponential- or Gaussian-like integrals.Comment: 12 page
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