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We study the following problem: given a regular symmetric form (linear functional) v, find all the regular symmetric forms u which satisfy the equation x 3 u = λ x v , λ ∈ C − { 0 }. We give the second-order recurrence relation of the orthogonal polynomial sequence with respect to u. Moreover, in the case where v is a semi-classical form of class s, we show that u is semi-classical and its class is analyzed in term of the class of v. An example is highlighted. [ABSTRACT FROM AUTHOR]

This paper deals with Mellin–Barnes integral, representing solution to thenth degree algebraic equation. We prove convergence of this integral in the boundary points of its convergence domain. The cases of tetranomial and pentanomial equations are completely studied. [ABSTRACT FROM PUBLISHER]

□ We present a new approach to carry out transient analysis for Markov modulated fluid flows. The system of partial differential equations for the time-dependent distributions is transformed into a system of ordinary differential equations by Laplace transform. This system of ordinary differential equations is solved by means of decomposing its coefficient matrix into two parts, one with eigenvalues with negative real parts and the other with positive real parts. The results we obtained are equivalent, but in simpler form, to those of Ahn and Ramaswami, which are derived by probabilistic arguments. [ABSTRACT FROM PUBLISHER]