By considering a particular probabilistic scenario associated with coincidences, we are led to a family of functions akin to the modified Bessel function of the first kind. These are in turn solutions to a certain family of linear differential equations possessing structural similarities to the modified Bessel differential equation. The Stirling number triangle of the second kind arises quite n...

The question of whether the zero viscosity limit ν → 0 is identical to the no viscosity ν ≡ 0 case is investigated in a simple shell (GOY) model with only three shells. We find that it is possible to express two velocities in terms of Bessel functions. The third velocity function acts as a background. The relevant Bessel functions are infinitely oscillating as ν → 0 and are not analytic as func...

In physical problems often the modified Bessel functions Kniz) with complex argument z occur, or the Hankel functions of the first kind Hn\z) which are related to Kniz) hyKniz) = iir/2)in+1Hna\iz), with i = (-l)m. Computationally rapid and fairly exact procedures are available for the evaluation of these functions for real or imaginary argument either by recurrence, [1], [2], or by polynomial a...

In this note we give a generalization of a result of Aronszajn and Smith [l] concerning sections of exceptional sets for the spaces of Bessel potentials on Rn of L2 functions and restrictions of functions in these spaces. For the sake of completeness we recall briefly the relevant definitions and theorems. We refer for details to [2]. Throughout this paper we will be concerned with functions de...

‎The sequences of the form ${E_{mb}g_{n}}_{m‎, ‎ninmathbb{Z}}$,‎ ‎where $E_{mb}$ is the modulation operator‎, ‎$b>0$ and $g_{n}$ is the‎ ‎window function in $L^{2}(mathbb{R})$‎, ‎construct Fourier-like‎ ‎systems‎. ‎We try to consider some sufficient conditions on the window‎ ‎functions of Fourier-like systems‎, ‎to make a frame and find a dual‎ ‎frame with the same structure‎. ‎We also extend t...

In this paper, we present the q-Lidstone polynomials which are q-Bernoulli generated by third Jackson q-Bessel function, based on Green’s function of a certain q-difference equation. Also, provide q-Fourier series expansions these and derive some results related to them.

This paper presents a method of evaluation of four integrals of Howland type, which involve a Bessel function in the integrands. With the aid of tabulated values, they are evaluated to 10D. Two of the four Howland integrals needed in the evaluation are evaluated anew to 20D in order to provide adequate accuracy. In a recent investigation of certain problems in elasticity concerning elliptic bou...

In this present study, we investigate the solutions for fractional kinetic equations involving k-Struve function using the Sumudu transform. The graphical interpretations of the solutions involving k-Struve function and its comparison with generalized Bessel function are given. The methodology and results can be considered and applied to various related fractional problems in mathematical physics.

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t In this paper, we give a set of sufficient conditions for the normalized form of the generalized Bessel func...