The bilateral birth–death chain generated by the associated Jacobi polynomials

نویسندگان

چکیده

We give a probabilistic interpretation of the associated Jacobi polynomials, which can be constructed from three-term recurrence relation for classical polynomials by shifting integer index n real number t. Under certain restrictions, this will rise to doubly infinite tridiagonal stochastic matrix, interpreted as one-step transition probability matrix discrete-time bilateral birth–death chain with state space on Z $\mathbb {Z}$ . also study unique UL and LU factorizations well discrete Darboux transformations corresponding spectral matrices. Finally, we use all these results provide an urn model integers polynomials.

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ژورنال

عنوان ژورنال: Studies in Applied Mathematics

سال: 2023

ISSN: ['0022-2526', '1467-9590']

DOI: https://doi.org/10.1111/sapm.12605