Ramon Edgar Moore and Alexander M. Gofen introduced a generalization of Joseph Liouville's concept elementary functions. even defined two variants these, viz. scalar generalized functions vector functions, formulated conjecture concerning them. We prove that, for some modified conjectures, the classes are different.

Some estimates are proved for the generalized Fourier-Bessel transform in the space (L^2) (alpha,n)-index certain classes of functions characterized by the generalized continuity modulus.

Most widely used special functions, such as orthogonal polynomials, Bessel Airy etc., are defined solutions to differential equations with polynomial coefficients. This class of functions is referred D-finite functions. There many symbolic algorithms (and implementations thereof) operate these objects exactly. Recently, we have extended this notion a more general that also allows for good handl...

Scaling level-spacing distribution functions in the “bulk of the spectrum” in random matrix models of N × N hermitian matrices and then going to the limit N → ∞, leads to the Fredholm determinant of the sine kernel sinπ(x− y)/π(x− y). Similarly a scaling limit at the “edge of the spectrum” leads to the Airy kernel [Ai(x)Ai′(y)−Ai′(x)Ai(y)] /(x − y). In this paper we derive analogues for this Ai...

In this paper, using a generalized translation operator, we prove theestimates for the generalized Fourier-Bessel transform in the space L2 on certainclasses of functions.