USFKAD is an encoded expert system for the eigenfunction expansion of solutions to the wave, diffusion, and Laplace equations: both homogeneous and nonhomogenous; one, two, or three dimensions; Cartesian, cylindrical, or spherical coordinates; Dirichlet, Neumann, Robin, or singular boundary conditions; in time, frequency, or Laplace domain. The user follows a menu to enter his/her choices and t...

we define a new function-valued inner product on l2(g), called ?-bracket product, where g is a locally compact abelian group and ? is a topological isomorphism on g. we investigate the notion of ?-orthogonality, bessel's inequality and ?-orthonormal bases with respect to this inner product on l2(g).

Methods for calculating the internal impedance of round wires are investigated. 'Exact' calculation using Kelvin Bessel functions runs into difficulties at radio frequencies due to rounding errors in computer floating-point arithmetic. Specialist techniques (such as the use of high-precision BCD arithmetic) could be used to circumvent this problem; but for general modelling, the use of approxim...

In this paper we study the duality of Bessel and g-Bessel sequences in Hilbert spaces. We show that a Bessel sequence is an inner summand of a frame and the sum of any Bessel sequence with Bessel bound less than one with a Parseval frame is a frame. Next we develop this results to the g-frame situation.

A generalized modular relation of the form $$F(z, w, \alpha )=F(z, iw,\beta )$$ , where $$\alpha \beta =1$$ and $$i=\sqrt{-1}$$ is obtained in course evaluating an integral involving Riemann $$\Xi $$ -function. This involves a surprising new generalization Hurwitz zeta function $$\zeta (s, a)$$ which we denote by _w(s, . We show that satisfies beautiful theory generalizing In particular, it sho...

This research includes the Bayesian estimation of parameters multivariate partial linear regression model when random error follows matrix-variate generalized modified Bessel distribution and found statistical test represented by finding Bayes factor criterion, predictive under assumption that shape are known. The prior about is non-informative information, as well simulate on generated data fr...

For integral representations of associated Legendre functions in terms of modified Bessel functions, we establish justification for differentiation under the integral sign with respect to parameters. With this justification, derivatives for associated Legendre functions of the first and second kind with respect to the degree are evaluated at odd-halfinteger degrees, for general complex-orders, ...

An approximate, closed-form expression for the value of the integral encountered inthe calculation ofthe probability density function (PDF) of the envelope of a partially saturated ocean acoustic process i obtained. Furthermore, an expression of this PDF as a series of modified Bessel functions i presented. The results may also be directly applied to the evaluation of the PDF encountered in the...

We establish the inverse Lebedev expansion with respect to parameters and arguments of the modified Bessel functions for an arbitrary function from Hardy’s space H2,A, A> 0. This gives another version of the Fourier-integral-type theorem for the Lebedev transform. The result is generalized for a weighted Hardy space Ĥ2,A ≡ Ĥ2((−A,A);|Γ(1+Rez+iτ)|2dτ), 0 < A < 1, of analytic functions f(z),z = R...

The topological degree of a continuous mapping is implemented for the calculation of the total number of the simple real zeros within any interval of the Bessel functions of first and second kind and their derivatives. A new algorithm, based on this implementation, is given for the localization and isolation of these zeros. Furthermore, a second algorithm is presented for their computation empl...