We study the Narayana triangles and related families of polynomials. We link this study to Riordan arrays and Hankel transforms arising from a special case of capacity calculation related to MIMO communication systems. A link is established between a channel capacity calculation and a series reversion.

A type of bell-shaped compact high order window function ψ(x, y) is studied, and closed analytic and approximation formulas are derived for its Hankel transforms. Applications of these results are presented as fast algorithms for calculating dyadic Green’s functions for electromagnetic scattering in multilayered media. Numerical results in electromagnetics are provided to demonstrate the accura...

Copyright q 2012 Salvador Sánchez-Perales et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We show conditions for the existence, continuity, and differentiability of functions defined by ΓΓs ∞ −∞ ftgt, sdt, where f is a func...

Integral transforms play an important rôle in Analytic number theory, the part of Number theory where problems of a number-theoretic nature are solved by the use of various methods from Analysis. The most common integral transforms that are used are: Mellin transforms (Robert Hjalmar Mellin, 18541933), Laplace transforms (Pierre-Simon, marquis de Laplace, 1749-1827) and Fourier transforms (Jose...

Abstract Bieberbach’s conjecture was very important in the development of geometric function theory, not only because result itself, but also due to large amount methods that have been developed search its proof. It is this context integral transformations type $f_{\alpha }(z)=\int _{0}^{z}(f(\zeta )/\zeta )^{\alpha }\,d\zeta $ <mml:msub...