A representation of Jacobi functions

E. Y. Deeba and E. L. Koh

International Journal of Mathematics and Mathematical Sciences, 1985, vol. 8, 1-11

Abstract:

Recently, the continuous Jacobi transform and its inverse are defined and studied in [1] and [2]. In the present work, the transform is used to derive a series representation for the Jacobi functions P λ ( α , β ) ( x ) , − ½ ≤ α , β ≤ ½ , α + β = 0 , and λ ≥ − ½ . The case α = β = 0 yields a representation for the Legendre functions and has been dealt with in [3]. When λ is a positive integer n , the representation reduces to a single term, viz., the Jacobi polynomial of degree n .

Date: 1985
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:746943

DOI: 10.1155/S0161171285000795

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