In this paper we introduce two polynomial sequences first one is Bivariate Bi- periodic
Jacobsthal polynomial which is define as ?????
(?, ?) = ????(?, ?)???????(?, ?) + 2?(?)???????(?, ?) if ???? is
even and ?????
(?, ?) = ????(?, ?)???????(?, ?) + 2?(?)???????(?, ?) if ???? is odd with initial conditions
?????(?, ?) = 0 and ?????(?, ?) = 1 and second one is Bivariate Bi- periodic Jacobsthal Lucas
polynomials which is define as ??
(?, ?) = ????(?, ?)????(?, ?) + 2?(?)????(?, ?) if ???? is even
and ??
(?, ?) = ????(?, ?)????(?, ?) + 2?(?)????(?, ?) if ???? is odd for ???? ? 2 with initial
conditions ??(?, ?) = 2, ??(?, ?) = ????(?, ?). We have found generating function and Binet’s
formula of both the polynomial sequences. Investigate relationship between Bivariate Biperiodic Jacobsthal and Bivariate Bi- periodic Jacobsthal Lucas polynomials. Also find wellknown Cassini’s identity, Catalan’s identity and discuss the converging properties of both the
polynomial sequences.
Keywords: Bi-variate Bi-periodic Jacobsthal polynomials, Bi-variate Bi-periodic Jacobsthal
Lucas polynomial, Cassini’s identity, Catalan’s identity, Binet’s formula, Generating function
Publication date: 01/12/2021
https://ijbpas.com/pdf/2021/December/MS_IJBPAS_2021_DEC_SPCL_2013.pdf
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https://doi.org/10.31032/IJBPAS/2021/10.12.2013
