傑克遜q貝塞爾函數

傑克遜q貝塞爾函數是英國數學家傑克遜在20世紀初創立的3個特殊函數,它們是貝塞爾函數的q模擬。定義如下

傑克遜q貝塞爾函數是通過階乘冪基本超幾何函數定義的:


參考文獻

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  • 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