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文章基本信息

  • 标题:A representation of Jacobi functions
  • 本地全文:下载
  • 作者:E. Y. Deeba ; E. L. Koh
  • 期刊名称:International Journal of Mathematics and Mathematical Sciences
  • 印刷版ISSN:0161-1712
  • 电子版ISSN:1687-0425
  • 出版年度:1985
  • 卷号:8
  • 期号:4
  • 页码:707-717
  • DOI:10.1155/S0161171285000795
  • 出版社:Hindawi Publishing Corporation
  • 摘要:

    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 .

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