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杰克逊q贝塞尔函数

杰克逊q贝塞尔函数是英国数学家杰克逊在20世纪初创立的3个特殊函数,它们是贝塞尔函数的q模拟。定义如下

杰克逊q贝塞尔函数是通过阶乘幂基本超几何函数定义的:


参考文献编辑

  • Ismail, Mourad E. H., The zeros of basic Bessel functions, the functions Jν +ax(x), and associated orthogonal polynomials, Journal of Mathematical Analysis and Applications, 1982, 86 (1): 1–19, ISSN 0022-247X, MR 649849, doi:10.1016/0022-247X(82)90248-7 
  • Jackson, F. H., On generalized functions of Legendre and Bessel, Transactions of the Royal Society of Edinburgh, 1903, 41: 1–28 
  • Jackson, F. H., Theorems relating to a generalization of the Bessel functions, Transactions of the Royal Society of Edinburgh, 1903, 41: 105–118 
  • Jackson, F. H., Theorems relating to a generalization of Bessel's function., Transactions of the Royal Society of Edinburgh, 1904, 41: 399–408, JFM 36.0513.02, doi:10.1017/s0080456800034475 
  • Jackson, F. H., The Application of Basic Numbers to Bessel's and Legendre's Functions, Proceedings of the London Mathematical Society, 1905, 2 (1): 192–220, doi:10.1112/plms/s2-2.1.192 
  • Jackson, F. H., The Application of Basic Numbers to Bessel's and Legendre's Functions (Second paper), Proceedings of the London Mathematical Society, 1905, 3 (1): 1–23, doi:10.1112/plms/s2-3.1.1