Ravi Bhukya | Skuniversity - Academia.edu (original) (raw)
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Papers by Ravi Bhukya
ln this paper, the Ultraspherical matrix polynomials are introduced starting from the hypergeomet... more ln this paper, the Ultraspherical matrix polynomials are introduced starting from the hypergeometric matrix function. The generating matrix function, an explicit representation, threeterm matrix recurrence relations and differential recurrence relations are given. We derive the Rodrigues’s formula and orthogonality properties for the Ultraspherical matrix polynomials. Finally, the expansions of the Ultraspherical matrix polynomials in a series of Hermite and Laguerre matrix polynomials are established. AMS Mathematics Subject Classification(2010): 25A50, 33C05, 33C25, 33C50, 33D45, 42C05.
Abstract: The main aim in this paper, we use the differential operators and matrix polynomial set... more Abstract: The main aim in this paper, we use the differential operators and matrix polynomial sets, generating matrix functions, integrals representation to derive the properties of Hermite matrix polynomials. Finally, we obtain an expansion of Hermite matrix polynomials in a series of Laguerre matrix polynomials and the Christoffel's formula of summation is established.
Studia Universitatis Babes-Bolyai Matematica
In the paper, by virtue of the Hölder integral inequality, the authors derive some inequalities o... more In the paper, by virtue of the Hölder integral inequality, the authors derive some inequalities of the Turán type for confluent hypergeometric functions of the second kind, for the Mellin transforms, and for the Laplace transforms, and improve some known inequalities of the Turán type.
ln this paper, the Ultraspherical matrix polynomials are introduced starting from the hypergeomet... more ln this paper, the Ultraspherical matrix polynomials are introduced starting from the hypergeometric matrix function. The generating matrix function, an explicit representation, threeterm matrix recurrence relations and differential recurrence relations are given. We derive the Rodrigues’s formula and orthogonality properties for the Ultraspherical matrix polynomials. Finally, the expansions of the Ultraspherical matrix polynomials in a series of Hermite and Laguerre matrix polynomials are established. AMS Mathematics Subject Classification(2010): 25A50, 33C05, 33C25, 33C50, 33D45, 42C05.
Abstract: The main aim in this paper, we use the differential operators and matrix polynomial set... more Abstract: The main aim in this paper, we use the differential operators and matrix polynomial sets, generating matrix functions, integrals representation to derive the properties of Hermite matrix polynomials. Finally, we obtain an expansion of Hermite matrix polynomials in a series of Laguerre matrix polynomials and the Christoffel's formula of summation is established.
Studia Universitatis Babes-Bolyai Matematica
In the paper, by virtue of the Hölder integral inequality, the authors derive some inequalities o... more In the paper, by virtue of the Hölder integral inequality, the authors derive some inequalities of the Turán type for confluent hypergeometric functions of the second kind, for the Mellin transforms, and for the Laplace transforms, and improve some known inequalities of the Turán type.