An analysis is presented of the torsional vibration of a rigid disc embedded to the surface of a transversely isotropic elastic half space. By using Hankel transform the mixed boundary value problem transform into a dual integral equation, which then transform to a Fredholm integral equation. After reduction to a Fredholm’s integral equation of second kind, solutions to the problem are obtained...

I. abstract. In this note, we prove several multiplicative products of the n-dimensional Hankel transform. In fact the following formulae: H{δ (k) (u(x))}.H{δ () (u(x))} = DH δ (k++ n−2 2) (u(x)) , (III,1)

In the present work we introduce a finite integral transform involving combination of Bessel functions as kernel under prescribed conditions. The corresponding inversion formula and some properties of this transform have also been given. Three problems of heat conduction in an infinite, a semi-infinite and a finite circular cylinder bounded by given surfaces with radiation-type boundary value c...

The method of realizing certain self-reciprocal transforms as (absolute) scattering, previously presented in summarized form in the case of the Fourier cosine and sine transforms, is here applied to the self-reciprocal transform f(y) 7→ H(f)(x) = ∫∞ 0 J0(2 √ xy)f(y) dy, which is isometrically equivalent to the Hankel transform of order zero and is related to the functional equations of the Dede...

We study families of generalized Catalan numbers, defined by convolution recurrence equations. We explore their relations to series reversion, Riordan array transforms, and in a special case, to Somos-4 sequences via the mechanism of the Hankel transform.