The Matrix Version for the Multivariable Humbert Polynomials

Some New Results for the Multivariable Humbert Polynomials

In this paper, we present some miscellaneous properties of the multivariable Humbert polynomials whose special cases include some well-known multivariable polynomials such as Chan-Chyan-Srivastava, Lagrange-Hermite and Erkus-Srivastava multivariable polynomials. We give recurrence relations, addition formula and integral representation for them. Then, we obtain some partial differential equatio...

On a Family of Multivariate Modified Humbert Polynomials

This paper attempts to present a multivariable extension of generalized Humbert polynomials. The results obtained here include various families of multilinear and multilateral generating functions, miscellaneous properties, and also some special cases for these multivariable polynomials.

A fractional type of the Chebyshev polynomials for approximation of solution of linear fractional differential equations

In this paper we introduce a type of fractional-order polynomials based on the classical Chebyshev polynomials of the second kind (FCSs). Also we construct the operational matrix of fractional derivative of order $ gamma $ in the Caputo for FCSs and show that this matrix with the Tau method are utilized to reduce the solution of some fractional-order differential equations.

On Humbert matrix function of two complex variables under differential operator

Higher rank numerical ranges of rectangular matrix polynomials

In this paper, the notion of rank-k numerical range of rectangular complex matrix polynomials are introduced. Some algebraic and geometrical properties are investigated. Moreover, for ϵ > 0; the notion of Birkhoff-James approximate orthogonality sets for ϵ-higher rank numerical ranges of rectangular matrix polynomials is also introduced and studied. The proposed denitions yield a natural genera...