Generalized harmonic numbers,Jacobi numbers and a Hankel determinant evaluation |
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Authors: | Wathek Chammam |
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Affiliation: | Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Majmaah, Saudi Arabia |
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Abstract: | In this paper we will introduce a sequence of complex numbers that are called the Jacobi numbers. This sequence generalizes in a natural way several sequences that are known in the literature, such as Catalan numbers, central binomial numbers, generalized catalan numbers, the coefficient of the Hilbert matrix and others. Subsequently, using a study of the polynomial of Jacobi, we give an evaluation of the Hankel determinants that associated with the sequence of Jacobi numbers. Finally, by finding a relationship between the Jacobi numbers and generalized harmonic numbers, we determine the evaluation of the Hankel determinants that are associated with generalized harmonic numbers. |
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Keywords: | Catalan numbers Hankel determinant orthogonal Jacobi polynomial generalized harmonic numbers |
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