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New representations of the Voigt functions

Pathan M., Shahwan M.

Demonstratio Mathematica

2006

Vol. 39, nr 1

75-80

This paper aims at some representations of generalized Voigt functions and their extensions in terms of series and integrals which are specially useful in situations when the parameters take on particular values. Explicit representations of these functions are given in terms of familiar special functions of one and two variables. The Voigt integrals and series resulting in connections with the Lommel, Struve, Laguerre and parabolic cylinder functions and ultimately the Kampe de Feriet function will follow as natural consequences for analytical evaluations and uses.

Strong maximum principles for implicit parabolic functional-differential problems together with nonstandard inequalities with sums

Byszewski L.

Demonstratio Mathematica

2005

Vol. 38, nr 4

857--866

The aim of the paper is to give strong maximum principles for implicit parabolic functional - differential problems together with nonstandard inequalities with sums in relatively arbitrary (n + 1)-dimensional time-space sets more general than the cylindrical domain. The results obtained can be applied in the theory of diffusion and in the theory of heat conduction.